Нелинейная динамика — междисциплинарная наука, в которой изучаются свойства нелинейных динамических систем. Нелинейная динамика использует для описания систем нелинейные модели, обычно описываемые дифференциальными уравнениями и дискретными отображениями.Нелинейная динамика включает в себя теорию устойчивости, теорию динамического хаоса, теорию интегрируемых систем.
World Scientific Publishing, Singapore, 1993, 158 Pages This is a series of lecture notes on nonlinear dynamics for physicists. The level is that of an advanced undergraduate or beginning graduate student. The main aim of these lectures is to present a balance of qualitative and quantitative material. The book also aims to address three main questions about nonlinear dynamics:...
Berlin: De Gruyter, 2022. — 373 p. This completely revised and updated edition of the one variable part of the author's classic older book "Iteration Theory of Holomorphic Maps on Taut Manifolds" presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a...
Springer, 2023. — 157 p. — ISBN 978-3-031-31662-3. Предположение о декодировании случайного аддитивного шума: аппаратная перспектива This book gives a detailed overview of a universal Maximum Likelihood (ML) decoding technique, known as Guessing Random Additive Noise Decoding (GRAND), has been introduced for short-length and high-rate linear block codes. The interest in short...
Springer International Publishing AG, 2018. — 238 p. — ISBN: 3319781928. This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in...
Springer International Publishing AG, 2018. — 224 p. — ISBN: 3319781928. This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in...
Cambridge University Press, 2011. — 362 p. — ISBN 978-1-10766-410-4.
The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg-de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class...
Addison-Wesley, 1992. — 642 p. — (Studies in Nonlinearity). — ISBN: 0-20156-717-2. The book shows a new way to learn a new mathematics - it is a visual tour that's accessible to a wide range of academic levels. During the Renaissance, algebra was resumed from Near Eastern sources, and geometry from the Greek. Scholalrs of the time became familiar with classical mathematics....
Springer, Switzerland, 2021. — 284 p. — ISBN 978-3-030-53005-1. This book commemorates the 60th birthday of Dr. Wim van Horssen, a specialist in nonlinear dynamic and wave processes in solids, fluids and structures. In honor of Dr. Horssen’s contributions to the field, it presents papers discussing topics such as the current problems of the theory of nonlinear dynamic processes...
Springer, 2020. — 426 p. Motivated by recent increased activity of research on time scales, the book provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales. Researchers and graduate students who are interested in the method of Lyapunov functions/functionals, in the study...
New York: Springer, 2014. - 297 p. This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems...
Boca Raton: CRC Press, 2025. — 435 p. Preface Editors Contributors Elements of Time Scales Calculus First-Order Functional Dynamic Equations Foundations of Linear Control Theory on Time Scales Optimal Control Theory for Dynamic Equations Controllability of Dynamic Equations Delayed Dynamic Equations with sp-Terms Integro-Dynamic System with Stepanov-like Coefficients Terminal...
New York: Springer, 2010. — 189 p. Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential...
Springer, 2017. — 175 p. — (Nonlinear Physical Science). — ISBN: 978-981-10-3179-3. This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied...
Boston: Springer, 1997. — 270 p. In the long run of a dynamical system, after transient phenomena have passed away, what remains is recurrence. An orbit is recurrent when it returns repeatedly to each neighborhood of its initial position. We can sharpen the concept by insisting that the returns occur with at least some prescribed frequency. For example, an orbit lies in some...
Academic Press, 2020. — 380 p. — ISBN: 978-0-12-822855-5. This book is intended for system specialists interested in dynamic systems that operate at different time scales. The book discusses several types of errors and their propagation, covering numerical methods—including convergence and consistence properties and characteristics—and proving of related theorems within the...
New York: Springer, 1996. - 612 pp. На англ. яз. Chaos: An Introduction to Dynamical Systems is a new textbook aimed at introducing the world of nonlinear dynamics and chaos to students in mathematics and the sciences. The authors' goal is to explain the basic concepts in a way that reflects the wide range of influences present during the development of nonlinear dynamics, from...
Springer, 2020. — 283 p. — (Lecture Notes in Mathematics 2274). — ISBN: 978-3-030-55215-2. This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the...
Springer, 2023. — 250 p. This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors. A fundamental concept...
Basel: Birkhauser, 2005. — 274 p. The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations.
Springer, Switzerland, 2024. — 150 p. — ISBN 978-3-031-73163-1. This book provides a unifying approach to the study of statistical laws, critically evaluating their role in the theoretical understanding of complex systems and the different data-analysis methods used to evaluate them. Statistical laws describe regular patterns observed in diverse scientific domains, ranging from...
Cham: Springer, 2021. — 266 p. This monograph offers a coherent, self-contained account of the theory of Sinai–Ruelle–Bowen measures and decay of correlations for nonuniformly hyperbolic dynamical systems. A central topic in the statistical theory of dynamical systems, the book in particular provides a detailed exposition of the theory developed by L.-S. Young for systems...
New York: Springer, 2018. — 252 p. This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly...
New York: Springer, 2010. — 254 p. The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular...
Cham: Springer, 2022. — 73 p. This brief provides unified methods for the stabilization of some fractional evolution systems, nicely complementing existing literature on fractional calculus. The volume is divided into three chapters, the first of which considers the stabilization for some abstract evolution equations with a fractional damping, the second of which validates the...
Cham: Springer, 2023. — 159 p. Bifurcation theory is a major topic in dynamical systems theory with profound applications. However, in contrast to autonomous dynamical systems, it is not clear what a bifurcation of a nonautonomous dynamical system actually is, and so far, various different approaches to describe qualitative changes have been suggested in the literature. The aim...
Boston: Kluwer, 2000. — 215 p. Stochastic Resonance: Theory and Applications deals with the theory of noise-added systems and in particular with Stochastic Resonance, a quite novel theory that was introduced in the 1980s to provide better understanding of some natural phenomena (e.g. ice age recurrence). Following the very first works, a number of different applications to both...
Springer International Publishing AG, 2017. — 297 p. — (Contributions to Statistics) — ISBN: 978-3-319-55845-5. This volume collects latest methodological and applied contributions on functional, high-dimensional and other complex data, related statistical models and tools as well as on operator-based statistics. It contains selected and refereed contributions presented at the...
Springer, 2007. — 461 p. This book is a complete treatise on the theory of nonlinear dynamics of chaotic and stochastic systems. It contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results in a field to which the authors have made important contributions themselves. Despite the unified presentation of the...
Springer, 2014. - 300 p. - This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of...
New York: John Wiley & Sons, 2003. — 254 p. The time operator is a powerful method for the study of unstable dynamics and chaos theory. This synthesis of classical and modern material provides a highly applied approach to the development of both spectral analysis and prediction for chaotic complex systems for which the time operator is described by a semigroup of operators.
Taylor & Francis, 2002. - 580 pages.
The field of nonlinear dynamics and low-dimensional chaos has developed rapidly over the past twenty years. The principal advances have been in theoretical aspects but more recent applications in a wide variety of the sciences have been made. Nonlinear Dynamics and Chaos in Semiconductors is the first book to concentrate on specific physical...
Berlin: de Gruyter, 2021. — 288 p. The authors present a completely new and highly application-oriented field of nonlinear analysis. The work covers the theory of non-smooth input-output systems and presents various methods to non-standard applications in mathematics and physics. A particular focus lies on hysteresis and relay phenomena, electric circuits with diode...
Springer, 2018. — 340 p. The present book is the second volume and it is dedicated to nonlinear physics. This is a very large area of research including subjects as regulation and morphogenesis of living systems, nonlinear hydrodynamic waves, gravitational waves, ocean circulation, drug resistance, black holes, brain tumors, antifreeze proteins, dark matter waves, neural...
Springer, 2011. — 327 pages. The ECCOMAS Thematic Conference Multibody Dynamics 2009 was held in Warsaw, representing the fourth edition of a series which began in Lisbon (2003), and was then continued in Madrid (2005) and Milan (2007), held under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). The conference provided a forum for...
B.: Springer, 2010. - 591p. The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are...
2nd edition. — Springer, 1986. — 119 p. — ISBN-13 978-3-540-16199-8. The first information on catastrophe theory appeared in the western press about ten years ago. In magazines like "News week" there were reports of a revolution in mathematics, com parable perhaps to Newton's invention of the differential and integral calculus. It was claimed that the new science, catas trophe...
Springer International Publishing AG, 2017. — 336 p. — (Nonlinear Systems and Complexity 20) — ISBN: 9783319536729. This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M. I....
Cambridge University Press, 1990. — 79 p. — ISBN: 0521303621, 0521316502. Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit "chaotic behavior." The first portion of the book is based on lectures given at the University of London and covers the background to...
Chapman & Hall, 1992. - 330 pages.
In recent years there has been unprecedented popular interest in the chaotic behavior of discrete dynamical systems. The ease with which a modest microcomputer can produce graphics of extraordinary complexity has fired the interest of mathematical-minded people from pupils in schools to postgraduate students. At undergraduate level, there is a...
Chapman & Hall, 1992. - 330 pages. This text discusses the qualitative properties of dynamical systems including both differential equations and maps, The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams to develop the material including a treatment of chaotic behaviour. The unprecedented popular interest shown in...
Journal. Open Academic Press. 2013 — 496 p. Introduction - Norma B. Crosby Theoretical Models of SOC Systems - Markus J. Aschwanden SOC and Fractal Geometry - R. T. James McAteer Percolation Models of Self-Organized Critical Phenomena - Alexander V. Milovanov Criticality and Self-Organization in Branching Processes: Application to Natural Hazards - Álvaro Corral, Francesc...
Berlin/Boston, Germany: Walter de Gruyter GmbH, 2016. — 149 p. — ISBN: 3110460866. This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Duality of the almost periodic and proximal relations Limit directions of...
Springer, Berlin, 2008. — 485 p. — ISBN 978-3-540-74357-6. This book is a tribute to Prof. Alberto Isidori on the occasion of his 65th birthday. Prof. Isidori’s prolific, pioneering and high-impact research activity has spanned over 35 years. Throughout his career, Prof. Isidori has developed ground-breaking results, has initiated research directions and has contributed towards...
Cambridge University Press, 1995. — 308 p. — ISBN: 0521452430, ISBN13: 9780521452434. In this book, the authors present the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems, and they extend the theory to include vector exponential series. The first part of the book presents the modern theory of...
Springer, 2018. — 411 p. — (Springer Proceedings in Mathematics & Statistics 248). — ISBN: 978-3-319-96597-0. This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life...
Amsterdam: Springer, 2008. — 342 p. This volume contains the invited papers presented at the 9th International Conference Dynamical Systems Theory and Applications held in Lódz, Poland, December 17-20, 2007, dealing with nonlinear dynamical systems. The conference brought together a large group of outstanding scientists and engineers, who deal with various problems of dynamics...
Singapore: World Scientific, 2007. - 320p.
This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in...
Springer, 1998. — 316 p. How well is Nature simulated by the varied asymptotic models that imaginative scientists have invented? This book deals with asymptotic methods in nonlinear dynamics. For the first time a detailed and systematic treatment of new asymptotic methods in combination with the Pade approximant method is presented. Most of the basic results included in this...
InTech, 2012. - 355 p. - This book focuses on introducing both theoretical and application oriented approaches in science and engineering. It is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos. Applications of 2D Pade...
Springer, 2004. — 341 p. — ISBN: 978-3-642-05810-3. This monograph is devoted to recent advances in nonlinear dynamics of continuous elastic systems. A major part of the book is dedicated to the analysis of non-homogeneous continua, e.g. plates and shells characterized by sudden changes in their thickness, possessing holes in their bodies or/and edges, made from different...
Singapore: World Scientific, 2021. — 561 p. In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related...
Springer, 2021. — 355 p. — (Springer Proceedings in Mathematics & Statistics). — ISBN 978-3-030-77313-7. This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference “Dynamical Systems: Theory and Applications”, held in Łódź, Poland on December 2-5, 2019. The wide...
Berlin: Walter de Gruyter, 2023. - 214 p. - ISBN 3110677865. Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at...
Academic Press, 2018. — 718 p. — (Advances in Nonlinear Dynamics and Chaos). — ISBN: 978-0-12-816152-4. This book consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms,...
Elsevier, 2018. — 680 p. — ISBN: 978-0-12-813592-1. This book illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order...
Springer, 2017. — 877 p. — ISBN: 978-3-319-50249-6. The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories,...
Springer, 2006. — 277 p. — (Understanding Complex Systems). — ISBN 978-3-540-34822-1. Emergent свойства в естественных и искусственных динамических системах An important part of the science of complexity is the study of emergent properties arising through dynamical processes in various types of natural and artificial systems. This is the aim of this book, which is the outcome...
Amsterdam: Springer, 1995. — 201 p. This is the second and final issue of the collection of papers that were contributed by friends and colleagues of (Late) Professor P. R. "Pat" Sethna of the University of Minnesota to commemorate his 70th birthday on May 26, 1993. The first set of contributions was published in Nonlinear Dynamics as the last issue (no. 6) of Vol. 4 in 1993....
Cambridge University Press, 1996, 255 p. Books that take you from undergraduate physics to a nontrivial understanding of nonlinear dynamics, chaos and fractals are rare. Chaotic Dynamics does the job ellegantly. The familiar pendulum is used to illustrate the basic techniques and concepts in nonlinear dynamics. The reader is gently introduced to phase diagrams, Poincare sections,...
N.-Y.: Springer, 2008. - 284p.
This book is an introduction to the multidisciplinary field of anomalous diffusion in complex systems, with emphasis on the scaling approach as opposed to techniques based on the quantitative analysis of underlying transport equations. Typical examples of such systems are turbulent plasmas, convective rolls, zonal flow systems and stochastic...
3rd Edition. — NY, USA: W. H. Freeman and Company, 2014. — 756 p. — ISBN: 3906980472. Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems...
Springer New York Dordrecht Heidelberg London, 2012. X, 310 p. — ISBN: 978-1-4614-0456-9, e-ISBN: 978-1-4614-0457-6 Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s...
John Wiley & Sons Ltd, West Sussex, UK, 2016. — 306 p. — ISBN: 1119015642. Arun K. Banerjee is one of the foremost experts in the world on the subject of flexible multibody dynamics. This book describes how to build mathermatical models of multibody systems with elastic components. Examples of such systems include the human body itself, construction cranes, cares with trailers,...
Boca Raton: CRC Press, 2019. — 207 p. Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the...
Acknowledgements. ntroduction. The chaos game. Attractors of iterated function systems. Another chaos game. Codes, metrics and topologies. ntroduction. Points and spaces. Functions, mappings and transformations. Addresses and code spaces. Metric spaces. Metrics on code space. Cauchy sequences, limits and continuity. Topological spaces. mportant basic topologies. Some key...
Springer Science+Business Media, New York, 2013. — 296 p. — ISBN: 0817683992 This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals,...
Birkhauser, 2010. - 440 p. - This book - an outgrowth of an international conference held in honor of Jacques Peyrière - provides readers with an overview of recent developments in the mathematical fields related to fractals. Included are original research contributions as well as surveys written by experts in their respective fields. The chapters are thematically organized...
Springer International Publishing AG, 2017. — 320 p. — (Trends in Mathematics) — ISBN: 978-3-319-57803-3. The fractals in mathematics are old. The first examples from the end of the nineteenth century are probably Cantor’s ternary set and the graphs of continuous nowhere differentiable functions of Riemann, Weierstrass and others. The main tools for studying fractals are...
Basel: Birkhäuser, 2008. — 301 p. The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and...
Springer, 2013. — 155 p. — (Springer Monographs in Mathematics). — ISBN: 978-3-319-00547-8. The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it...
Berlin: Springer, 2012. — 303 p. Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension...
Cambridge: Cambridge University Press, 2007. — 264 p. This book presents the theory of dynamical systems with nonzero Lyapunov exponents, offering a rigorous mathematical foundation for deterministic chaos - the appearance of "chaotic" motions in pure deterministic dynamical systems. These ideas and methods are used in many areas of mathematics as well as in physics, biology,...
American Mathematical Society, 2023. — 354 p. This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential...
Springer, 2019. — 222 p. — (Problem Books in Mathematics). — ISBN: 3030159140. This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Aimed at the graduate/upper undergraduate level, the emphasis is on dynamical systems with discrete time. In addition to the basic theory, the...
Springer, 2012. — 213 p. — ISBN: 1447148347
The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a...
Springer, 2024. — 139 p. This book presents the reader with a streamlined exposition of the notions and results leading to the construction of normal forms and, ultimately, to the construction of smooth conjugacies for the perturbations of tempered exponential dichotomies. These are exponential dichotomies for which the exponential growth rates of the underlying linear dynamics...
Springer, 1990. — 229 p. Proceedings of the 6th Interdisciplinary Workshop on Nonlinear Coherent Structures in Physics, Mechanics, and Biological Systems Held at Montpellier, France, June 21–23, 1989. This book is devoted to the applications of the mathematical theory of solitons to physics, statistical mechanics, and molecular biology. It contains contributions on the signature...
New York: Wiley-ISTE, 2013. - 506 p. This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities. The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal...
Singapore: World Scientific, 1998. — 215 p. A brief outline of the ideas and methods of mathematical modelling of populations Growth dynamics of isolated population Predator-prey interaction Competition and symbiosis Local systems of three populations Dissipative structures in predator-prey systems.
Oxford: Oxford University Press, 1991. — 385 p. This volume originated as a series of lectures given at the workshop Hyperbolic Geometry and Ergodic Theory' held at the International Centre for Theoretical Physics in Trieste, 17-28 April, 1989. Hyperbolic geometry and surfaces of negative curvature were crucial to the early development of ergodic theory, so the two subjects have a...
Springer, 2024. — 376 p. — (Understanding Complex Systems). — ISBN 978-3-031-40680-5. The book covers a large class of nonlinear systems with many practical engineering applications. The approach is based on the extension of linear systems theory using the Volterra series. In contrast to the few existing treatments, our approach highlights the algebraic structure underlying...
Springer, 2017. — 284 p. — ISBN: 978-3-319-50763-7. This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is...
Springer Science & Business Media, 2002. — 227 p. Chaos theory plays an important role in modern physics and related sciences, but -, the most important results so far have been obtained in the study of gravitational systems applied to celestial mechanics. The present set of lectures introduces the mathematical methods used in the theory of singularities in gravitational...
Philadelphia: SIAM, 2017. — 433 p. Many physical, chemical, biomedical, and technical processes can be described by means of partial differential equations (PDEs) or dynamical systems. If the underlying processes exhibit nonlinear dynamics, analysis and prediction of the complex behavior is often only possible by solving the (partial) differential equations numerically. For this...
Springer, Switzerland, 2019. — 185 p. — ISBN 978-3-030-11145-8. Observer Design for Nonlinear Systems deals with the design of observers for the large class of nonlinear continuous-time models. It contains a unified overview of a broad range of general designs, including the most recent results and their proofs, such as the homogeneous and nonlinear Luenberger design...
Oxford University Press, 2005. — 404 p. Covering a broad range of topics, this text provides a comprehensive survey of the modeling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this a unique text in the midst of many current books on chaos and...
Springer, 2015. — 338 p.
Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a...
Cambridge University Press, 2003. — 272 p. — (London Mathematical Society Lecture Note Series 310). — ISBN13: 978-0-511-06556-9. This collection of survey papers by leading researchers in ergodic theory and low-dimensional and topological dynamics comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory,...
Springer, 2007, 304 pages This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group and self-consistent mode coupling. Dynamic critical phenomena near a second order...
American Mathematical Society, 1927. — 305 p. Physical aspects of dynamical systems. Variational principles and applications. Formal aspects of dynamics. Stability of periodic motions. Existence of periodic motions. Application of Poincare's geometric theorem. General theory of dynamical systems. The case of two degrees of freedom. The problem of three bodies.
American Mathematical Society, 1927. — 316 p. His research in dynamics constitutes the middle period of Birkhoff's scientific career, that of maturity and greatest power. Yearbook of the American Philosophical Society The author's great book is well known to all, and the diverse active modern developments in mathematics which have been inspired by this volume bear the most...
Springer International Publishing AG, 2018. — 120 p. — (SpringerBriefs in Applied Sciences and Technology). – ISBN: 3319709925. This book describes systematic design techniques for chaotic and hyperchaotic systems, the transition from one to the other, and their implementation in electronic circuits. It also discusses the collective phenomena manifested by these systems when...
Springer-Verlag Berlin Heidelberg 1998. — (Theoretical and Mathematical Physics). — 350 pp. — ISBN: 978-3-642-63780-3 (Print) 978-3-642-58893-8 (Online).
This is a modern approach to Hamiltonian systems where multi-Hamiltonian systems are presented in book form for the first time. These systems allow a unified treatment of finite, lattice and field systems. Having more than one...
Cham: Springer, 2022. — 114 p. This book provides a comprehensive survey of the Sharkovsky ordering, its different aspects and its role in dynamical systems theory and applications. It addresses the coexistence of cycles for continuous interval maps and one-dimensional spaces, combinatorial dynamics on the interval and multidimensional dynamical systems. Also featured is a...
De Gruyter, 1994. — 284 p. Preface Basic Concepts Equations for oscillatory systems The shift operator and first return function Integral and integrofunctional operators for periodic problem The harmonic balance method The method of mechanical quadratures The collocation method The method of finite differences Factor methods Existence theorems for oscillatory regimes Smooth...
Cambridge University Press, 2018. — 266 p. — ISBN: 978-1-107-05626-8. A modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled...
Amsterdam: Elsevier, 2008. — 256 p. The origin of the word synchronization is a greek root, meaning ''to share the common time''. The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of...
New York: Springer, 2016. - 201p. These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan...
Birkhäuser Boston, 2001. — 369 pages. The study of dynamic equations on a measure chain (time scale) goes back to its founder S. Hilger (1988), and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on measure chains can build bridges between continuous and discrete mathematics. Further, the study of...
Boston: Birkhäuser, 2012. — 369 p. The study of dynamic equations on a measure chain (time scale) goes back to its founder S. Hilger (1988), and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on measure chains can build bridges between continuous and discrete mathematics. Further, the study of...
Springer, 1980. — 374 p. This book contains the papers presented at the ICM2002 Satellite Conference on Nonlinear Evolution Equations and Dynamical Systems. About 50 mathematicians and scientists attended the meeting — including E. Witten (IAS), C. Nappi (Princeton), K. Khanin (Cambridge), D. Phong (Columbia), d'Hoker (UCLA) and Peng Chiakuei (CAS). The book covers several fields,...
Mahwah: Psychology Press, 2007. — 148 p. — ISBN: 9780805850123, 0805850120. Each volume in the Notre Dame Series on Quantitative Methodology features leading methodologists and substantive experts who provide instruction on innovative techniques designed to enhance quantitative skills in a substantive area. This latest volume focuses on the methodological issues and analyses...
Berlin: de Gruyter, 2018. — 414 p. This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work...
Philadelphia: Society for Industrial and Applied Mathematics (SIAM), 2013. — 376 p. Until recently, measurable dynamics has been held as a highly theoretical mathematical topic with few generally known obvious links for practitioners in areas of applied mathematics. However, the advent of high-speed computers, rapidly developing algorithms, and new numerical methods has allowed...
2nd Edition. — Springer International Publishing, Switzerland, 2017. — 286 p. — (Understanding Complex Systems) — ISBN: 9783319424958 The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the...
Springer, 2009. 198 p. ISBN 978-3-642-00936-5 Paradigm for Chaos Main Features of Chaotic Systems Reconstruction of Dynamical Systems Controlling Chaos Synchronization of Chaotic Systems Stochastic Resonance The Appearance of Regular Fluxes Without Gradients
Springer, 2010. — 406 p. What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to...
Springer, 2005 — 390 p.
The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unified important developments and led to a remarkably successful theory for a large class of systems: uniformly hyperbolic systems often exhibit complicated evolution which, nevertheless, is now rather well understood, both geometrically and statistically. Another...
De Gruyter, 2017. — 299 p. The book provides a concise and rigor introduction to the fundamentals of methods for solving the principal problems of modern non-linear dynamics. This monograph covers the basic issues of the theory of integrable systems and the theory of dynamical chaos both in nonintegrable conservative and in dissipative systems. A distinguishing feature of the...
2nd Edition. — Springer, 2016. — 471 p. — (Progress in Mathematics 318). — ISBN: 3319338757. This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides...
Cambridge University Press, 2000. — 417 Pages This book explores the exciting new field of complexity. It features in-depth coverage of important theoretical areas, including fractals, chaos, nonlinear dynamics, artificial life, and self organization. It also provides overviews of complexity in several applied areas, including parallel computation, control systems, neural...
New York: Springer, 2021. — 201 p. This book presents a differential geometric method for designing nonlinear observers for multiple types of nonlinear systems, including single and multiple outputs, fully and partially observable systems, and regular and singular dynamical systems. It is an exposition of achievements in nonlinear observer normal forms.The book begins by...
Cambridge University Press, 2014. — 434 p. — (Cambridge Studies in Advanced Mathematics 141) — ISBN: 1107042917 Since its introduction in the early 1980s quasiconformal surgery has become a major tool in the development of the theory of holomorphic dynamics, and it is essential background knowledge for any researcher in the field. In this comprehensive introduction the authors...
Amsterdam: Springer, 1995. — 353 p. This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993. The vision of the institute was to illustrate the interplay between two important fields of Mathematics: Real Dynamical Systems and...
Cambridge: Cambridge University Press, 2017. — 234 p. Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such...
CRC, 2017. — 400 s. — ISBN: 978-1-4987-5596-2. This book covers the development of methods for detection and estimation of changes in complex systems. These systems are generally described by nonstationary stochastic models, which comprise both static and dynamic regimes, linear and nonlinear dynamics, and constant and time-variant structures of such systems. It covers both...
Springer, 2011. — xvi;313 p. — ISBN 978-1-4419-6869-2 (Print) 978-1-4419-6870-8 (Online).
Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices...
Oxford: Oxford University Press, 2018. — 425 p. This text is a high-level introduction to the modern theory of dynamical systems; an analysis-based, pure mathematics course textbook in the basic tools, techniques, theory and development of both the abstract and the practical notions of mathematical modelling, using both discrete and continuous concepts and examples comprising...
Cambridge: Cambridge University Press, 2012. — 313 p. One-dimensional dynamics has generated many results, and avenues of active mathematical research with numerous inroads to this research remain to be pursued by the advanced undergraduate or beginning graduate student. While much of the material in this book is not covered elsewhere, some aspects present new research topics...
Berlin: de Gruyter, 1994. — 376 p. Preface Basic notation Introduction Mathematical means The normal form of a Hamiltonian system The normal form of a linear system Nonlinear normalization Lowering the number of degrees of freedom Periodic and conditionally-periodic solutions Generalizations Notes Normalization of a Hamiltonian system near a cycle or a torus The normal form of...
ITexLi, 2021. — 117 p. — ISBN 1-83969-124-7, 978-1-83969-124-9, 1-83969-125-5, 978-1-83969-125-6. This book provides an overview of recent developments in the theory of dynamical systems, presenting some significant advances in the definition of new models, computer algorithms, and applications. Researchers, engineers and graduate students in both pure and applied mathematics...
Basel: Birkhäuser, 1997. — 138 p. This book grew out of the work developed at the University of Warwick, under the supervision of Ian Stewart, which formed the core of my Ph.D. Thesis. Most of the results described were obtained in joint work with Ian; as usual under these circumstances, many have been published in research journals over the last two years. Part of Chapter 3...
Basel: Birkhäuser, 2003. — 214 p. This book represents the latest developments on both the theory and applications of bifurcations with symmetry. It includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern...
Princeton University, UK, 2003. — 180 p. — (Princeton Series in Applied Mathematics) — ISBN10: 0691112983. Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are...
Berlin: Springer, 2002. — 493 p. Quasi-Conformal Geometry and Hyperbolic Geometry. On and Around the Bounded Cohomology of SL2. Densite d'orbites d'actions de groupes lineaires et proprietes d'equidistribution de marches aleatoires. Exceptional Sets in Dynamical Systems and Diophantine Approximation. An Introduction to Cocycle Super-Rigidity. Rigid Geometric Structures and...
American Mathematical Society, 2000. — 398 p. — (Graduate Studies in Mathematics 23) — ISBN: 0821808095. This is the first of two volumes on the qualitative theory of foliations. This volume is divided into three parts. It is extensively illustrated throughout and provides a large number of examples. Part 1 is intended as a "primer" in foliation theory. A working knowledge of...
American Mathematical Society, 2003. — 539 p. — (Graduate Studies in Mathematics 60) — ISBN: 0821808818. This is the second of two volumes on the qualitative theory of foliations. For this volume, the authors have selected three special topics: analysis on foliated spaces, characteristic classes of foliations, and foliated manifolds. Each of these is an example of deep...
Basel: Birkhäuser, 2013. — 287 p. — ISBN-13 9783034804806. — ISBN-10 3034804806. This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere,...
New York: Springer, 2017. — 266 p. This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in...
Springer-Verlag, 1993. - 201 pages. ISBN: 0387979425, 3540979425
A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary...
Cambridge: Cambridge University Press, 2017. — 574 p. This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about...
Springer, 1981. - 142 pages.
These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79.
The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is...
2nd Edition. — CRC Press, Taylor & Francis Group, 2019. — 281 p. — ISBN13: 978-0813341255. Catastrophe Theory was introduced in the 1960s by the renowned Fields Medal mathematician Rene' Thom as a part of the general theory of local singularities. Since then it has found applications across many areas, including biology, economics, and chemical kinetics. By investigating the...
CRC Press, 2023. — 393 p. — ISBN 978-1-032-35686-0. The art of applying mathematics to real-world dynamical problems such as structural dynamics, fluid dynamics, wave dynamics, robot dynamics, etc. can be extremely challenging. Various aspects of mathematical modelling that may include deterministic or uncertain (fuzzy, interval, or stochastic) scenarios, along with integer or...
CRC Press, 2023. — 393 p. — ISBN: 978-1-003-32803-2. The art of applying mathematics to real-world dynamical problems such as structural dynamics, fluid dynamics, wave dynamics, robot dynamics, etc. can be extremely challenging. Various aspects of mathematical modelling that may include deterministic or uncertain (fuzzy, interval, or stochastic) scenarios, along with integer or...
CRC Press, 2023. — 393 p. — ISBN: 978-1-003-32803-2. The art of applying mathematics to real-world dynamical problems such as structural dynamics, fluid dynamics, wave dynamics, robot dynamics, etc. can be extremely challenging. Various aspects of mathematical modelling that may include deterministic or uncertain (fuzzy, interval, or stochastic) scenarios, along with integer or...
CRC Press, 2023. — 393 p. — ISBN: 978-1-003-32803-2. The art of applying mathematics to real-world dynamical problems such as structural dynamics, fluid dynamics, wave dynamics, robot dynamics, etc. can be extremely challenging. Various aspects of mathematical modelling that may include deterministic or uncertain (fuzzy, interval, or stochastic) scenarios, along with integer or...
Cham: Springer, 2022. — 195 p. This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time...
World Scientific Publishing Company, 2004. - 528 pages.
The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to...
Springer, 2024. — 475 p. The monograph present ideas and methods, developed by the author, to solve the problem of existence of Bohr/Levitan almost periodic (respectively, almost recurrent in the sense of Bebutov, almost authomorphic, Poisson stable) solutions and global attractors of monotone nonautonomous differential/difference equations. Namely, the text provides answers to...
New York: Springer, 2020. — xxii, 434 p. — (Springer Monographs in Mathematics). — ISBN: 978-3-030-34292-0; ISBN: 978-3-030-34291-3. This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations. The content is developed over six chapters, providing a thorough...
Springer, 2024. — 114 p. — (Synthesis Lectures on Mathematics & Statistics). — ISBN 3031545044. This book provides a comprehensive review on tensor algebra, including tensor products, tensor unfolding, tensor eigenvalues, and tensor decompositions . Tensors are multidimensional arrays generalized from vectors and matrices, which can capture higher-order interactions within...
Singapore: World Scientific Publishing Company, 2023. — 233 p. — ISBN 9811278989. The topic of nonlinear systems is fundamental to the study of systems engineering. So extensive investigations have been carried out by both the nonlinear control and nonlinear dynamics communities, but the focus can be different — on controllers design and dynamics analysis, respectively. The...
Singapore: World Scientific, 2007. — 598 p.
This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a...
Singapore: World Scientific, 2009. — 357 p.
Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered...
Singapore: World Scientific, 2011. — 405 p.
Volume IV continues the author's odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing...
Singapore: World Scientific, 2002. — 112 p.
This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, or truth table, onto the point attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justified on firm ground. The...
Харьков: Аста, 2002. — 418 с. — ISBN: 966-7021-64-5, 966-7021-20-3. This book provides an exhaustive introduction to the scope of main ideas and methods of the theory of infinite-dimensional dissipative dynamical systems which has been rapidly developing in recent years. In the examples systems generated by nonlinear partial differential equations arising in the different...
Springer, 2021. — 389 p. — (IFSR International Series in Systems Science and Systems Engineering, 34). — ISBN 978-3030645328. This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are...
Springer, 2021. — 389 p. — (IFSR International Series in Systems Science and Systems Engineering, 34). — ISBN 978-3030645328. This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are...
Springer, 1999. — 219 p. This book deals with the theory of Poincaré--Birkhoff normal forms, studying symmetric systems in particular. Attention is focused on general Lie point symmetries, and not just on symmetries acting linearly. Some results on the simultaneous normalization of a vector field describing a dynamical system and vector fields describing its symmetry are presented...
New York: American Mathematical Society, 2014. — 303 p. This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in ℝd and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which...
Springer, 2015. — 239 p. Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about...
Berlin: Springer-Verlag , 1993. — 146 p. Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems. This book is an elaboration on some ideas of Gromov on hyperbolic spaces and hyperbolic groups in...
Springer London, 2016. — 192 p. — (Universitext). — ISBN: 144717285X. This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as...
Springer, 1999. — 457 p. — ISBN: 0387985123, 978-0387985121.
This volume gives an account of new and recent developments in the theory of random and, in particular, stochastic dynamical systems. Its purpose is to document and, to some extent, summarise the current state of the field of random dynamical systems beyond the recent monograph, "Random Dynamical Systems" by Ludwig...
Paris: Société Mathématique de France, 2020. — 364 p. This is the first of two volumes which celebrate the memory of JeanChristophe Yoccoz. These volumes present research articles on various aspects of the theory of dynamical systems and related topics that were dear to him. Keywords. — Annealed limit theorems, Birkhoff, blow-up, Cauchy distribution, chain-recurrence, chord...
Paris: Société Mathématique de France, 2020, — 364 p. This is the second of two volumes which celebrate the memory of Jean-Christophe Yoccoz. These volumes present research articles on various aspects of the theory of dynamical systems and related topics that were dear to him. Keywords. — Accessibility, analytic circle diffeomorphisms, Arnol0d- Liouville theorem, Birkhoff sums,...
Oxford: Oxford University Press, 2003. — 487 p. This is an assessment and review of progress in integrating evolutionary modelling and computation, molecular and developmental evolution, and nonlinear population dynamics into evolutionary theory. It brings together a wide range of eminent researchers in evolutionary dynamics in order to formulate a comprehensive theory that...
World Scientific, 2010. — 421 p. This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth...
Cambridge: Cambridge University Press, 1996. — 351 p. This book is devoted to the asymptotic properties of solutions of stochastic evolution equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical systems; invariant measures for stochastic evolution equations; and invariant measures for specific models. The focus is on models of dynamical...
Springer-Verlag Berlin Heidelberg, 2014. — 208 p. Research into social systems is challenging due to their complex nature. Traditional methods of analysis are often difficult to apply effectively as theories evolve over time. This can be due to a lack of appropriate data, or too much uncertainty. It can also be the result of problems which are not yet understood well enough in...
Springer, 2012. — 536 p. Characterizing Nonlinear Dynamic Systems. 2 Nonlinear Modeling of Squeeze-Film Phenomena. 3 Nonlinear Mathematical Modeling of Microbeam MEMS. 4 Complex Motions in a Fermi Oscillator. 5 Nonlinear Visco-Elastic Materials. 6 Nonlinear Dynamic Modeling of Nano and Macroscale Systems. 7 Equilibrium of a Submerged Body with Slack Mooring. 8 Nonlinear...
Springer Cham Heidelberg New York Dordrecht London, 2015. — XXIII, 324 p. 230 illus., 134 illus. in color. — ISBN: 978-3-319-09461-8, ISBN: 978-3-319-09462-5 (eBook). Explores the most up-to-date applications and underlying principles of nonlinear approaches to problems in engineering and physics, including sections on analytic nonlinearity and practical nonlinearity Enlightens...
Springer, 2018. — 456 p. This book is based on the same concept used in the previous volumes of the series Nonlinear Approaches in Engineering Applications, organized by the editors. Nonlinear analysis and approaches have been developed alongside the development and modelling of natural dynamic phenomena. Although the main approaches in the analysis of dynamic phenomena are still...
Springer-Verlag, 2011. — 189 p. — (Universitext). — ISBN: 085729072X. During the past thirty years, strong relationships have interwoven the fields of dynamical systems, linear algebra and number theory. This rapport between different areas of mathematics has enabled the resolution of some important conjectures and has in fact given birth to new ones. This book sheds light on...
World Scientific Pub Co Inc, 2004. — 572 p. — ISBN10: 9810230516. The book comprises a broad panorama of phenomena occurring in four major classes of radiophysical and mechanical systems - linear, nonlinear, parametric, and nonlinear-parametric. An analytical technique for the broad circle of issues under consideration is developed. It is presented in a user-friendly form,...
New York: Springer, 2020. — 176 p. This book gathers papers on recent advances in the ergodic theory of group actions on homogeneous spaces and on geometrically finite hyperbolic manifolds presented at the workshop “Geometric and Ergodic Aspects of Group Actions,” organized by the Tata Institute of Fundamental Research, Mumbai, India, in 2018. Written by eminent scientists, and...
Springer Nature Switzerland, 2022. — 243 p. — (Undergraduate Lecture Notes in Physics). — ISBN-13 9783030910310. This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear...
Springer, 1993. — 621 p. One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the...
Berlin: de Gruyter, 2014. — 516 p. There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate...
Springer, 2000. — 304 Pages. — ISBN: 3540521186 Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach allowing a clear focus on the essential mathematical structures. It brings out features common...
Perseus Books, 1992. — 320 p. — ISBN: 0201554062 A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It...
Westview Press, 1989. — 360 p.
The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text,...
3rd Edition. — Chapman and Hall/CRC, 2021 p. — 433 p. — ISBN 978-0-367-23615-1. There is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense...
Cambridge: Cambridge University Press, 2024. — 330 p. — ISBN 1009455621. Matrix theory is the lingua franca of everyone who deals with dynamically evolving systems, and familiarity with efficient matrix computations is an essential part of the modern curriculum in dynamical systems and associated computation. This is a master's-level textbook on dynamical systems and...
Springer-Verlag London Limited, 2008 — 496 p. Editors: S.S. Antman, J.E. Marsden, L. Sirovich. Many dynamical systems that occur naturally in the description of physical processes are piecewise-smooth. That is, their motion is characterized by periods of smooth evolutions interrupted by instantaneous events. Traditional analysis of dynamical systems has restricted its attention...
Atlantis Press, 2012. — 145 p. The guiding light of this monograph is a question easy to understand but difficult to answer: {What is the shape of the universe? In other words, how do we measure the shortest distance between two points of the physical space? Should we follow a straight line, as on a flat table, fly along a circle, as between Paris and New York, or take some...
B.: Springer, 2009. - 270p. Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the...
London: Academic Press, 1982. — 648 p. The study of the soliton as a stable particle-like state of nonlinear systems has so caught the imagination of physicists and mathematicians of all descriptions that it can genuinely claim to be one of the few interGisciplinary subjects of modern day mathematical physics. It may be that the topic of solitons will pass through this wide...
World Scientific Publishing Company, 2006. — 356 p. Von Neumann made fundamental contributions to Computing and he had a keen interest in Dynamical Systems, specifically Hydrodynamic Turbulence. This book, offering a state-of-the-art collection of papers in computational dynamical systems, is dedicated to the memory of von Neumann. Including contributions from J.E. Marsden,...
Springer, 2019. — 606 p. — (Pathways in Mathematics). — ISBN: 978-3-030-19372-0. This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field...
Cambridge University Press, 2011. — 404 p. — (New Mathematical Monographs: 18). This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger...
Basel: Birkauser, 2011. — 293 p. — ISBN: 978-3-0348-0014-3; e-ISBN: 978-3-0348-0015-0 Поризм Понселе — классическая теорема проективной геометрии. Она и ее многомерные обобщения, сформулированные Дарбу, тесно связаны с теорией динамических систем (интегрируемые биллиарды на конфокальном пучке квадрик) и алгебраической геометрией (теоремы сложения на гиперэллиптических...
Monograph. — Cambridge: Cambridge University Press, 1992. — XV, 323 p. A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated...
Cambridge: Cambridge University Press, 2022. — 593 p. This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution...
Basel: Birkhauser, 1991. — 471 p. This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come....
Reviews of Modern Physics, Vol.57.
Differentiable Dynamics and the Reconstruction of Dynamics from an Experimental Signal, Characteristic Exponents, Entropy and Information Dimension, Experimental Aspects.
New York: Springer, 2018. — 320 p. The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of...
Hoboken: Wiley, 2005. — 195 p. Exponential attractors is a new area of dynamical systems, pioneered by the authors of this book, and has become an extremely vigorous source of research both from the pure as well as applied and numerical points of view. Includes numerous applications for Navier-Stokes equations and many other related partial differential equations of mathematical...
Springer, 2005. — 152 p. Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these...
Springer, 2020. — 474 p. — ISBN: 978-3-030-26032-3. Experts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local...
London: Springer, 2011. — 497 p. This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include...
Springer Cham, Heidelberg, New York, Dordrecht, London, 2015. — 630 p. — (Graduate Texts in Mathematics 272) — ISBN: 3319168975. Stunning recent results by Host-Kra, Green-Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a...
Boca Raton: CRC Press, 2019. — 402 p. Review of chaotic dynamics -- Human Immunodeficiency Virus and urbanization dynamics -- Chaotic behaviors in piecewise linear mappings -- Robust chaos in neural networks models -- Estimating Lyapunov exponents of 2-D discrete mappings -- Control, synchronization and chaotification of dynamical systems -- Boundedness of some forms of...
Basel: Birkhäuser, 2010. — 271 p. Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces. This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schröder’s and Abel’s functional equations,...
London, Institute of Physics Publishing, 2003 - 327 стр. Microscopic Dynamics of Plasmas and Chaos discusses the resonant wave-particle interaction in plasmas, provides the tools for chaotic Hamiltonian dynamics, and describes a turbulent macroscopic system through the chaotic classical mechanics of the corresponding N-body problem. The book begins with the fundamentals of...
Springer Science & Business Media, 2006. — 609 p. This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on...
Springer, 2010. - 382 pages.
Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather...
3rd ed. — Boca Raton: CRC Press, 2018. — 618 p. Modeling and Analysis of Dynamic Systems, Second Edition introduces MatLAB, Simulink, and Simscape and then uses them throughout the text to perform symbolic, graphical, numerical, and simulation tasks. Written for junior or senior level courses, the textbook meticulously covers techniques for modeling dynamic systems, methods of...
Amsterdam: Springer, 2019. — 296 p. This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice problems are illustrated, which might be...
Boca Raton: CRC Press, 2018. — 599 p. Nonlinear Integrable Systems Systems of nonlinearly-coupled differential equations solvable Integrable nonlinear PDEs on the half-line Detecting discrete integrability: the singularity approach Elementary introduction to discrete soliton equations New results on integrability of the Kahan-Hirota-Kimura discretizations Solution Methods and...
New York: Chapman and Hall/CRC, 2019. — 541 p. Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its...
CRC Press, 2021. — 510 p. — ISBN 9780367541125. The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just...
UC Berkeley, 2006. — 139 pages.
These notes survey, without too many precise details, the basic theory of probability, random differential equations and some applications. A really careful treatment assumes the students' familiarity with probability theory, measure theory, ordinary differential equations, and partial differential equations as well. The author tried to design...
Springer, 2020. — 290 p. — ISBN: 981150492X. This book addresses privacy in dynamical systems, with applications to smart metering, traffic estimation, and building management. In the first part, the book explores statistical methods for privacy preservation from the areas of differential privacy and information-theoretic privacy (e.g., using privacy metrics motivated by mutual...
Princeton University Press, 2022. — 252 p. New mathematical research in arithmetic dynamics In The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools...
Academic Press, 2016. — 248 p. — ISBN: 978-0-12-804294-6. Poincare-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of...
Springer, 2011. - 390 pages. "Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving...
Princeton University Press, 2019. - 262 p. - (Primers in Complex Systems, 14). - ISBN: 0691161526. Chaos and Dynamical Systems presents an accessible , clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many...
Berlin: Springer, 2008. — 204 p. This pages include the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, our concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behavior and what synchronization phen- ena can be...
Singapore: World Scientific, 1992. — 550 p. Recent developments in nonlinear dynamics has significantly altered our basic understanding of the foundations of classical physics. However, it is quantum mechanics, not classical mechanics, which describes the motion of the nucleons, atoms, and molecules in the microscopic world. What are then the quantum signatures of the...
Singapore: World Scientific Publishing Company, 2006. — 226 p. This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and...
Springer, 2005. — 367 p. — ISBN: 3540281150. "Nonlinear Oscillations in Mechanical Engineering" explores the effects of nonlinearities encountered in applications in that field. Since the nonlinearities are caused, first of all, by contacts between different mechanical parts, the main part of this book is devoted to oscillations in mechanical systems with discontinuities caused...
Berlin: Springer-Verlag, 2001. — 815 p. This book summarizes and highlights progress in our understanding of Dy namical Systems during six years of the German Priority Research Program "Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems" . The program was funded by the Deutsche Forschungsgemeinschaft (DFG) and aimed at combining, focussing, and enhancing...
North-Holland, 2002. — 1099 p. — ISBN 0444501681, 9780080532844. This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that...
Paris: European Mathematical Society Publishing House, 2019. — 739 p. The origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a...
Springer, 1993. — 290 p. We start this book with Theme A (see Figure P. I in the Preface), which aims to develop an essential and fundamental understanding of systems science. So, what is systems science? When asked to explain what systems science is all about, many systems scientists are confronted with a rather daunting task. The discipline tends to be presented and...
Springer International Publishing, Switzerland, 2016. – 323. – ISBN10: 331930612X Includes the latest scientific developments in Multibody Dynamics State of the Art in this field Reflects the multidisciplinary character of the field This book includes selected papers from the ECCOMAS Thematic Conference on Multibody Dynamics, that took place in Barcelona, Spain, from June 29 to...
New York: Routledge, 2021. — 216 p. Discovering Dynamical Systems Through Experiment and Inquiry differs from most texts on dynamical systems by blending the use of computer simulations with inquiry-based learning (IBL). IBL is an excellent tool to move students from merely remembering the material to deeper understanding and analysis. This method relies on asking students...
New York: Springer, 2012. — 345 p. Parametric Resonance in Dynamical Systems discusses the phenomenon of parametric resonance and its occurrence in mechanical systems, vehicles, motorcycles, aircraft and marine craft, along micro-electro-mechanical systems. The contributors provides an introduction to the root causes of this phenomenon and its mathematical equivalent, the...
World Scientific Publishing, 2015. — 564 p. — Volume 1 of Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications. This is a collection of articles, many written by people who worked with Mandelbrot, memorializing the remarkable breadth and depth of his work in science and the arts. Contributors include mathematicians, physicists, biologists,...
Springer, 2018. — 112 p. — (Springer Briefs in Applied Sciences and Technology; SpringerBriefs in Nonlinear Circuits). — ISBN: 978-3-319-75956-2. This book addresses synchronization in networks of coupled systems. It illustrates the main aspects of the phenomenon through concise theoretical results and code, allowing readers to reproduce them and encouraging readers to pursue...
Springer, 2018. — 381 p. — (Pathways in Mathematics). — ISBN: 978-3-319-72277-1. The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming...
Springer, 2000. — 498 p. The theory of stochastic processes provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. Noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for as yet open problems (information transmission in the nervous system and information processing in the brain, processes at...
Springer, 2013. - 236 p. - With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as...
Springer, 2013. - 250 pages. ISBN: 3642335519
With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex...
2nd edition. — IOP Publishing, 2021. — 179 p. — ISBN 978-0-7503-3757-1. Written for students at upper-undergraduate and graduate levels, it is suitable for advanced physics courses on nonlinear physics. The book covers the fundamental properties of nonlinear waves, dealing with both theory and experiment. The aim is to emphasize established tools and introduce new methods...
Boca Raton: CRC Press, 2024. — 550 p. System Dynamics: Modeling, Simulation, and Response covers linearity-based modeling techniques before delving into nonlinear systems. It compares the Bond Graph technique against traditional techniques (Newton's law, Kirchhoff's law, the law of the conservation of energy, and the heat transfer law). Presenting transient response analyses of...
Springer, 2022. — 601 p. About the Editor-in-Chief About the Volume Editor Perturbation Theory Definition of the Subject Poincaré´s Theorem and Quanta Mathematics and Physics. Renormalization Need of Convergence Proofs Multiscale Analysis A Paradigmatic Example of PT Problem Lindstedt Series Convergence. Scales. Multiscale Analysis Non Convergent Cases Conclusion and Outlook...
Springer, 2017. — 193 p. — (Mathematical Physics Studies). — ISBN 978-3-319-54357-4. Лекции по Гипергамильтоновой Динамике This book provides the mathematical foundations of the theory of hyperhamiltonian dynamics, together with a discussion of physical applications. In addition, some open problems are discussed. Hyperhamiltonian mechanics represents a generalization of...
Singapore: World Scientific Pub Co Inc, 2000. — (Advanced Series in Nonlinear Dynamics: Volume 14). — 342 p. — ISBN: 978-9810241483. This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of...
Springer, 2007. - 303 pp. This volume reviews the current understanding of the Fermi-Pasta-Ulam (FPU) Problem without trying to force coherence on differing perspectives on the same problem by various groups or approaches. The contributions lead the interested but inexperienced reader through gradual understanding, starting from general analysis and proceeding towards more...
Springer, Berlin, 2007. — 158 p. — ISBN-10 3-540-36775-6. This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the fields of biology, demography, ecology, economics, engineering, finance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a...
Springer, 2011, 231 p. Wavelets: Theory and Applications for Manufacturing presents a systematic description of the fundamentals of wavelet transform and its applications. Given the widespread utilization of rotating machines in modern manufacturing and the increasing need for condition-based, as opposed to fix-interval, intelligent maintenance to minimize machine down time and...
Publisher: arXiv, 2011. - 150 pages. The goal of this set of lectures is to combine two seemingly unrelated topics: - The study of Boolean functions, a field particularly active in computer science; - Some models in statistical physics, mostly percolation. The link between these two fields can be loosely explained as follows: a percolation configuration is built out of a...
Paul van Geert, 1994. — 313 p. The forms of change. Developmental paths and systems. Observing and measuring dynamic processes. The dynamic growth model. Transitions and developmental fractals. Oscillations. Connected growers. Development and uncertainty. Building a model: a case history. The dynamics of mutual interaction. Epilogue: Towards an experimental theoretical...
Springer International Publishing AG, 2018. — 364 p. — ISBN: 3319739530. Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on...
Springer, 2019. — 886 p. — ISBN: 978-3-030-15419-6. This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics...
De Gruyter, 2023. — 337 p. — ISBN 978-3-11-118289-6. The latest advancements in time scale calculus are the focus of this book. New types of time-scale integral transforms are discussed in the book, along with how they can be used to solve dynamic equations. Novel numerical techniques for partial dynamic equations on time scales are described. New time scale inequalities for...
De Gruyter, 2023. — 337 p. — ISBN 9783111185194. The latest advancements in time scale calculus are the focus of this book. New types of time-scale integral transforms are discussed in the book, along with how they can be used to solve dynamic equations. Novel numerical techniques for partial dynamic equations on time scales are described. New time scale inequalities for...
Springer, 2021. — 882 p. — ISBN 978-3-030-76131-8. The theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. In some cases, there exists uncertainty, ambiguity, or vague factors in such problems, and fuzzy theory and interval analysis are powerful tools for modeling these...
Springer, 2021. — 882 p. — ISBN 978-3-030-76131-8. The theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. In some cases, there exists uncertainty, ambiguity, or vague factors in such problems, and fuzzy theory and interval analysis are powerful tools for modeling these...
Boca Raton: CRC Press/Chapman & Hall, 2022. — 175 p. Introduction to Traveling Waves is an invitation to research focused on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for...
2nd Edition. — Springer International Publishing, Switzerland, 2017. — 304 p. — ISBN10: 3319439421 After spending many years as a systems engineer for controlling various production processes, I began to view the world more and more as a collection of systems. In my engineering work, systems existed as manufacturing entities, such as chemical plants, oil refineries, food and...
2nd edition. — New York: Springer, 2016. — 304 p. Apply system knowledge at work and in daily life without deep mathematical knowledge Build models and simulate system behaviors on a personal computer Optimize systems in many different ways Reduce or eliminate unintended consequences Develop a holistic world view Systems are everywhere and we are surrounded by them. We are a...
Springer, 2015. - 239 pp. This book is a study of the interactions between different types of systems, their environment, and their subsystems. The author explains how basic systems principles are applied in engineered (mechanical, electromechanical, etc.) systems and then guides the reader to understand how the same principles can be applied to social, political, economic...
Springer, 2009. — 288 p. Papers in this collection partly represent the set of talks that were presented at Texas Tech University on the occasion of Daya’s memorial workshop in the year 2007. Daya had a varied interest in the field of Dynamics and Control Theory and the papers bring out the essence of his involvement in these activities. He also had a large number of...
Springer, 1997. — 217 p. The closed orbits of three-dimensional flows form knots and links. This book develops the tools - template theory and symbolic dynamics - needed for studying knotted orbits. This theory is applied to the problems of understanding local and global bifurcations, as well as the embedding data of orbits in Morse-Smale, Smale, and integrable Hamiltonian flows....
Dover Publications, 1993. — 680 p. Grounded in the work of Henri Poincare, R. Thom and others, catastrophe theory attempts to study how the qualitative nature of the solutions of equations depends on the parameters that appear in the equations. This advanced-level treatment describes the mathematics of catastrophe theory and its applications to problems in mathematics, physics,...
Springer, 2019. — 134 p. — (Advanced Courses in Mathematics CRM Barcelona). — ISBN: 978-3-030-23688-5. This book is aimed at mathematicians, scientists, and engineers, studying models that involve a discontinuity, or studying the theory of nonsmooth systems for its own sake. It is divided in two complementary courses: piecewise smooth flows and maps, respectively. Starting from...
Amsterdam: Springer, 1992. — 213 p. Regular and Chaotic Behaviour of Dynamical Systems Shocks in the Burgers Equation and the Asymmetric Simple Exclusion Process Automata Networks Strategies for Optimization Problems Two Chosen Examples for Fractals: One Deterministic, the Other Random A Brief Account of Statistical Theories of Learning and Generalization in Neural Networks On...
Boca Raton: CRC Press/Chapman & Hall, 2022. — 577 p. Applications of Fractional Calculus to Modeling in Dynamics and Chaos aims to present novel developments, trends, and applications of fractional-order derivatives with power law and Mittag-Leffler kernel in the areas of chemistry, mechanics, chaos, epidemiology, fluid mechanics, modeling, and engineering. Non-singular and...
Springer International Publishing Switzerland 2015. — 219 p. — (Nonlinear Systems and Complexity 11). — ISBN: 978-3-319-09866-1 (Print) 978-3-319-09867-8 (Online).
This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to...
N.-Y.: Springer, 2015. - 240p. This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The...
Dekker, 1977. — 224 p. — ISBN ISBN 0824764102, 9780824764104. Invited addresses . On the limiting equations and invariance of time-dependent difference equations. Liapunov functions and boundedness of solutions. Recent results on oscillation of solutions of forced and perturbed nonlinear differential equations of even order. Contractive mappings and periodically perturbed...
Springer International Publishing, Switzerland, 2016. — 313 p. — (Developments in Mathematics) — ISBN: 3319448463. This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results...
Springer International Publishing, Switzerland, 2016. — 313 p. — (Developments in Mathematics) — ISBN: 3319448463. This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results...
5th ed. — Springer, 2024. — 467 p. — ISBN 3031550757. This textbook offers a comprehensive introduction to the concepts underpinning our modern understanding of complex and emergent behavior. Mathematical methods necessary for the discussion are introduced and explained on the run . All derivations are presented step-by-step . This new fifth edition has been fully revised and...
4th edition. — Cham; Heidelberg; New York; Dordrecht; London: Springer, 2015. — XVI, 422 p. — ISBN: 978-3-319-16264-5; ISBN: 978-3-319-16265-2 (eBook). This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are...
Springer, 2010. - 325 pages.
Discover a wide range of findings in quantitative complex system science that help us make sense of our complex world. Written at an introductory level, the book provides an accessible entry into this fascinating and vitally important subject.
Proceedings of the NATO Advanced Study Institute held at the University of Warwick, Coventry, England, 27 August–6 September, 1974 -312 c.
The first international conference on differential games was held at Amherst, Massachusetts, in September 1969. Asecond meeting, partially supported by N.A.T.O., was held in Varenna, Italy, in June 1970. At these conferences many new...
Berlin, Springer, 2003. — 343 p. Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. As a new and young discipline, chaos control has in effect come into play with many traditional scientific and technological advances today. Automatic control theory and practice, on the other hand, is a traditional and long-lasting...
Springer, 1983. — 471 p. This book applied the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking the cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer...
Providence: American Mathematical Society. 2012. — 322 p. This volume contains the proceedings of the AMS Special Session on Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, in honor of Ronald Mickens's 70th birthday, held January 9–10, 2013, in San Diego, CA. Included are papers on design and analysis of discrete-time and continuous-time dynamical...
Springer, 2019. — 605 p. — (Communications and Control Engineering). — ISBN: 978-3-030-12480-9. Control of Wave and Beam PDEs is a concise, self-contained introduction to Riesz bases in Hilbert space and their applications to control systems described by partial differential equations (PDEs). The authors discuss classes of systems that satisfy the spectral determined growth...
Springer, 2023. — 110 p. — (Synthesis Lectures on Mechanical Engineering). — ISBN 978-3-031-17882-5. This book builds on the fundamental understandings, learned in undergraduate engineering and physics in principles of dynamics and control of mechanical systems. The design of real-world mechanical systems and devices becomes far more complex than the spring-pendulum system to...
Springer, 2023. — 1611 p. — (Synthesis Lectures on Mechanical Engineering). — ISBN 978-3-031-17883-2. This book builds on the fundamental understandings, learned in undergraduate engineering and physics in principles of dynamics and control of mechanical systems. The design of real-world mechanical systems and devices becomes far more complex than the spring-pendulum system to...
Springer International Publishing AG, part of Springer Nature, 2017. — 411 p. — (Springer Proceedings in Mathematics & Statistics 205) — ISBN: 978-3-319-64172-0. Dynamical systems as a field have had tremendous impact across mathematics and the sciences that goes far beyond the in-depth study and classification of the qualitative behavior of flows and terations. The...
Springer International Publishing AG, part of Springer Nature, 2017. — 411 p. — (Springer Proceedings in Mathematics & Statistics 205) – ISBN: 978-3-319-64172-0. Dynamical systems as a field have had tremendous impact across mathematics and the sciences that goes far beyond the in-depth study and classification of the qualitative behavior of flows and terations. The...
Princeton University Press, 2008. — 976 p.
Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed...
Mathematics Institute, The University of Warwick.
Definition of a Markov Process, Dynamical Systems, Stationary Markov Processes, Main Structure theorem, Existence of an Invariant Measure, A Simple Yet Powerful Uniqueness Criterion, Hormander’s Condition, What About the Infinite-Dimensional Case? , The Bismut-Elworthy-Li Formula, The Asymptotic Strong Feller Property.
A Macroscopic Approach to Complex System
Germany, Springer, 2000 - 232 p.
This book presents the concepts needed to deal with self-organizing complex systems from a unifying point of view that uses macroscopic data. The various meanings of the concept "information" are discussed and a general formulation of the maximum information (entropy) principle is used. With the aid of...
London: CRC Press, 2000. — 297 p. The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many...
Dover Publications, 2015. — 180 p. By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and...
Springer, 1991. — 581 p. The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications with perhaps...
Springer, 1991. — 577 p. — (Texts in Applied Mathematics 3) — ISBN: 1461287650. The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has...
Springer, 2002. - 293 pages.
From the reviews of the second edition: "This book presents a contemporary geometric theory of infinite-dimensional dynamical systems where the major emphasis is on retarded functional-differential equations. … Each chapter contains some abstract theorems but the authors give some examples as well illustrating these general results and having...
Cambridge: Cambridge University Press, 2023. — 427 p. Transport barriers are observed inhibitors of the spread of substances in flows. The collection of such barriers offers a powerful geometric template that frames the main pathways, or lack thereof, in any transport process. This book surveys effective and mathematically grounded methods for defining, locating and leveraging...
Springer, 1999. — 430 p. — (Applied Mathematical Sciences, 138). — ISBN: 0-387-98697-9. Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled with instabilities, can result in highly irregular behavior. This book gives a unified treatment of resonant...
Springer International Publishing AG, 2017. — 121 p. — (SpringerBriefs in Mathematics) — ISBN: 978-3-319-61933-0. Numerical dynamics is concerned with how well a numerical scheme applied to a differential equation replicates the dynamical behaviour of the dynamical system generated by the differential equation, in particular its long-term or asymptotic behaviour. This...
Springer, 2010. - 340 pages. ISBN: 0857291114 An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and...
Springer, 2020. — 504 p. — (Springer Monographs in Mathematics). — ISBN: 978-3-030-32067-6. This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in...
Elsevier, 2010. - 560 Pages. In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent...
North Holland, 2002. — 1233 p. — ISBN 0444826696. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable...
Elsevier Science, 2006. — 1235 p. — ISBN 0444520554, 9780444520555. This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey "Principal Structures” of Volume 1A. The present volume contains...
Cambridge University Press, 2003. — 435 p. — ISBN 0521587506, 9780521587501. The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite...
Princeton: Princeton University Press, 1986. - 410p.
This book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, it remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields.
Springer, 2025. - 968 p. - ISBN 9819761123. This textbook contains about 200 fully solved problems in analytical and numerical methods for nonlinear osccillations. These comprise all the end-of-chapter problems in Ali H. Nayfeh and Dean T. Mook’s famous textbook "Nonliear Oscillations" (John Wiley & Sons, New York, 1995) . Mathematical software are adopted to make those...
New York: AMS, 2014. - 209p.
Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology. This book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed dynamical systems with a weak inhomogeneity given...
New York: Academic Press. 1974. — 358 pages. This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.
Oxford University Press, 2014. — 112 p. — ISBN 0199662541, 9780199662548. The importance of complexity is well-captured by Hawking's comment: "Complexity is the science of the 21st century". From the movement of flocks of birds to the Internet, environmental sustainability, and market regulation, the study and understanding of complex non-linear systems has become highly...
Oxford University Press, 2014. — 112 p. — (Very Short Introductions). The importance of complexity is well-captured by Hawking's comment: "Complexity is the science of the 21st century". From the movement of flocks of birds to the Internet, environmental sustainability, and market regulation, the study and understanding of complex non-linear systems has become highly influential...
Springer-Verlag, 1994. — 225 p. An increasing number of colleges and universities are offering undergraduate courses in discrete dynamical systems. This growth is due in part to the proliferation of inexpensive and powerful computers, which have provided access to the interesting and complex phenomena that are at the heart of dynamics. A second reason for introducing dynamics...
Springer-Verlag, 1994. — 225 p. An increasing number of colleges and universities are offering undergraduate courses in discrete dynamical systems. This growth is due in part to the proliferation of inexpensive and powerful computers, which have provided access to the interesting and complex phenomena that are at the heart of dynamics. A second reason for introducing dynamics...
Springer-Verlag Berlin, 2006, 318 pages This classic text, an often-requested reprint, develops and explains the foundations of noise-induced processes. At its core is a self-contained, textbook-style presentation of the elements of probability theory, of the theory of Markovian diffusion processes and of the theory of stochastic differential equations, on which the modeling of...
Монография, Springer, London, 2009, 357р. Today, chaos is no longer a stranger to many. Instead, chaos theory and technology. have gradually become well known as a promising research field with significant. mpacts on an increasing number of novel, potentially attractive, time- and energycritical engineering applications. Overview. The Origin and Development of Chaos Theory....
ITexLi, 2023. — 92 p. — ISBN 1837684367 9781837684366 1837684359 9781837684359 1837684375 9781837684373. The field of mathematics has produced many beautiful results, and among them, fixed points hold great importance as they can be used to describe and explain various mathematical curiosities, even those of the most complex technical applications. This book explores some of...
Monograph. — Springer, 2009. — 297 p.
Vibro-impact dynamics has occupied a wide spectrum of studies by dynamicists, physicists, and mathematicians. These studies may be classified into three main categories: modeling, mapping and applications. The main techniques used in modeling of vibro-impact systems such as phenomenological modelings, Hertzian models, and non-smooth...
3rd Edition. — Springer, 2019. — 607 p. — (Applied Mathematical Sciences 149). — ISBN: 978-3-030-21472-2. This book provides a modern static imperfect bifurcation theory applicable to bifurcation phenomena of physical and engineering problems and fills the gap between the mathematical theory and engineering practice. Systematic methods based on asymptotic, probabilistic, and...
Springer-Verlag New York 2010. — 2nd Ed. — (Applied Mathematical Sciences 149). — 520 pp. — ISBN: 978-1-4419-7075-6 (Print) 978-1-4419-7296-5 (Online). This book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods - based on asymptotic, probabilistic, and group-theoretic standpoints - are used to examine...
Springer, 2009. — 490 pages. ISBN: 3540856315 This edited book is aimed at interdisciplinary device-oriented applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators,...
New York: Springer, 2017. — 359 p. This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications...
Springer-Verlag New York 2011. — (Applied Mathematical Sciences 178). — 174 pp. — ISBN: 978-1-4614-0334-0 (Print) 978-1-4614-0335-7 (Online). The book presents the recently introduced and already widely cited semi-discretization method for the stability analysis of delayed dynamical systems with parametric excitation. Delay-differential equations often come up in different...
New York: Springer, 2010. - 307 p. This book is devoted to complexity understanding and management, considered as the main source of efficiency and prosperity for the next decades. Divided into six chapters, the book begins with a presentation of basic concepts as complexity, emergence and closure. The second chapter looks to methods and introduces polystochastic models, the wave...
N.-Y.: Springer, 2008. - 844p. Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on...
New York: Springer, 2006. — 841 p. This volume presents a comprehensive introduction into rigorous geometrical dynamics of complex systems of various natures. By "complex systems", in this book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a unified geometrical approach to dynamics of complex systems of...
Basel: Birkhäuser, 2012. — 221 p. This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading...
Springer, 2016. — 428 p. The book focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic...
Springer, 2014. — 430 pages. ISBN: 1461468760.
Nonlinear Approaches in Engineering Applications 2 focuses on the application of nonlinear approaches to different engineering and science problems. The selection of the topics for this book is based on the best papers presented in the ASME 2010 and 2011 in the tracks of Dynamic Systems and Control, Optimal Approaches in Nonlinear...
Springer, 2018. — 531 p. — ISBN: 978-3-030-02106-1. The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to...
Springer, 2020. — 104 p. — (Frontiers in Applied Dynamical Systems: Reviews and Tutorials 07). — ISBN: 978-3-030-35986-7. This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth’ definition. A review of...
Springer, 2021. — 939 p. — ISBN 978-3-030-75451-8. This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous...
Springer, 2021. — 939 p. — (Interdisciplinary Applied Mathematics 53). — ISBN 978-3-030-75451-8. This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of...
CRC Press, Taylor & Francis Group, 2019. — 400 p. — ISBN13: 978-1-4987-1926-1. Engineering dynamics and vibrations has become an essential topic for ensuring structural integrity and operational functionality in different engineering areas. However, practical problems regarding dynamics and vibrations are in many cases handled without success despite large expenditures. This...
Springer, 2023. — 307 p. This book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the...
New York: Springer, 2016. — 515 p. This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral...
New York: ITAe, 2011. - 537p. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. The contribution of the book enlarges the field of the Discrete-Time Systems with...
Springer, Dordrecht, 2014. — 352 p. — ISBN 978-94-007-6774-4. Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear...
Cambridge University Press, 2010. — 182 p. — (Cambridge Studies in Advanced Mathematics 122) — ISBN: 978-0-521-19440-2. This informal introduction provides a fresh perspective on isomorphism theory, which is the branch of ergodic theory that explores the conditions under which two measure preserving systems are essentially equivalent. It contains a primer in basic measure...
Cambridge: Cambridge University Press, 2002. — 208 p. This monograph offers a broad investigative tool in ergodic theory and measurable dynamics. The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the...
2nd edition. — Cambridge University Press, 2003. — 388 p. — ISBN: 0521821509 The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be...
2 edition. — Cambridge University Press, 2003. — 388 p. — ISBN: 0521821509 The time variability of many natural and social phenomena is not well described by standard methods of data analysis. However, nonlinear time series analysis uses chaos theory and nonlinear dynamics to understand seemingly unpredictable behavior. The results are applied to real data from physics,...
Academic Press, 1996. — 164 p. — ISBN: 9780123968401, 0123968402. More than two decades of intensive studies on non-linear dynamics have raised questions on the practical applications of chaos. One possible answer is to control chaotic behavior in a predictable way. This book, oneof the first on the subject, explores the ideas behind controlling chaos. The book explains, using...
New York: Springer, 1995. — 437 p. Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the...
American Mathematical Society, 2023. — 366 p. This book challenges and intrigues from beginning to end. It would be a treat to use for a capstone course or senior seminar. --William J. Satzer, MAA Reviews on Glimpses of Soliton Theory (First Edition) Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading...
Basel: Birkhäuser, 2000. — 278 p. This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type"...
Cambridge: Cambridge University Press, 1996. — 824 p. This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental...
London: CRC Press, 2002. — 256 p. Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov`s method. The analysis focuses on dynamic...
World Scientific, 1984. — 252 p. This publication collates the lectures and papers delivered at the meeting on "The theory of dynamical systems and its applications to nonlinear problems" held at the Research Institute for Mathematical Sciences of Kyoto University in Kyoto, Japan, from July 4 to 7, 1984. The twenty lectures are classified into four groups: dynamical systems,...
Springer International Publishing, Switzerland, 2013. — 290 p. — (Lecture Notes in Mathematics 2089) — ISBN: 3319012878 This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one...
American Mathematical Society, 2010. — 245 p. — (Mathematical Surveys and Monographs). — ISBN: 0821848941. The original motivation for this work came from the study of certain results in ergodic theory, primarily, but not exclusively, obtained over the last several years. These included: i) Work of Hjorth and Foreman-Weiss concerning the complexity of the problem of...
Springer, 2020. — 544 p. In this work, outstanding, recent developments in various disciplines, such as structural dynamics, multiphysic mechanics, computational mathematics, control theory, biomechanics, and computer science, are merged together in order to provide academicians and professionals with methods and tools for the virtual prototyping of complex mechanical systems....
Springer Netherlands, 1994. — XVI, 672 p. — (An International Book Series on The Fundamental Theories of Physics, v. 61). This monograph is devoted to an entirely new branch of nonlinear physics – solitary intrinsic states, or autosolitons, which form in a broad class of physical, chemical and biological dissipative systems. Autosolitons are often observed as highly...
New York: Springer, 2017. — 455 p. This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing,...
Springer, 2016. — 521 p. The book is the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Nonlinear Oscillations Nonlinear Simulation Using Harmonic Balance Nonlinear Modal...
Springer, 2016. — 414 p. Nonlinear Dynamics, Volume 1. Proceedings of the 34th IMAC, A Conference and Exposition on Dynamics of Multiphysical Systems: From Active Materials to Vibroacoustics, 2016, the first volume of ten from the Conference, brings together contributions to this important area of research and engineering. Th e collection presents early findings and case...
Springer, 2017. — 220 p. Nonlinear Dynamics, Volume 1: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics,...
Springer, 2019. — 421 p. Nonlinear Dynamics, Volume 1: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018, the first volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics,...
Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014. — Springer Cham Heidelberg New York Dordrecht London, 2014, VIII, 319 p. 256 illus., 208 illus. — ISBN: 978-3-319-04521-4, ISBN: 978-3-319-04522-1 (eBook), DOI 10.1007/978-3-319-04522-1in color. — (Conference Proceedings of the Society for Experimental Mechanics Series). This critical...
Kevin M. Pilgrim - Combinations of Complex Dynamical Systems (Lecture Notes in Mathematics). Springer. 2003, 120 pages. The goal of this research monograph is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain...
Springer, 2019. — 328 p. — (Nonlinear Systems and Complexity 26). — ISBN: 978-3-030-11838-9. This book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the \phi^4 model has been the basis for a broad array of...
Springer, 2020. — 389 p. — (Nonlinear Systems and Complexity 32). — ISBN: 978-3-030-44991-9. This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal...
3rd edition. — Pearson, 2001. — 750 p. This text is intended for a first-year graduate-level course on nonlinear systems or control. It may also be used for self study or reference by engineers and applied mathematicians. It is an outgrowth of my experience teaching the nonlinear systems course at Michigan State University, East Lansing. Students taking this course have had...
3rd edition. — Pearson, 2001. — 241 p. This text is intended for a first-year graduate-level course on nonlinear systems or control. It may also be used for self study or reference by engineers and applied mathematicians. It is an outgrowth of my experience teaching the nonlinear systems course at Michigan State University, East Lansing. Students taking this course have had...
New York: Springer, 2004. — 278 p. On Applications of P -Adic Analysis P -Adic Numbers and P -Adic Analysis P -Adic Dynamical Systems Perturbation of Monomial Systems Dynamical Systems in Finite Extensions of ℚ p Conjugate Maps P -Adic Ergodicity P -Adic Neural Networks Dynamics in Ultra-Pseudometric Spaces Random Dynamics Dynamics of Probability Distributions on the P -Adic...
University of Michigan Press, 2004. — 397 p. Chaos Theory in the Social Sciences: Foundations and Applications offers the most recent thinking in applying the chaos paradigm to the social sciences. The book explores the methodological techniques—and their difficulties—for determining whether chaotic processes may in fact exist in a particular instance and examines implications...
Springer-Verlag New York 2012. — 2nd Ed. — (Applied Mathematical Sciences 156). — 400 pp. — ISBN: 978-1-4614-0501-6 (Print) 978-1-4614-0502-3 (Online).
In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as...
Springer, 1987. — 457 p. The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study...
Springer, 2015. — 295 p. — (Lecture Notes in Mathematics 2140). — ISBN: 978-3-319-17520-1. Extending Griffiths’ classical theory of period mappings for compact Kähler manifolds, this book develops and applies a theory of period mappings of “Hodge-de Rham type” for families of open complex manifolds. The text consists of three parts. The first part develops the theory. The...
New York: Springer, 1997. - 254p.
Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined...
World Scientific Publishing, 2012. — 400 pages. — ISBN10: 9814340588 This volume provides the latest developments in the field of fractional dynamics, which cover fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important...
Hoboken: Wiley, 2015. — 499 p. Craig Kluever's Dynamic Systems: Modeling, Simulation, and Control highlights essential topics such as analysis, design, and control of physical engineering systems, often composed of interacting mechanical, electrical and fluid subsystem components. The major topics covered in this text include mathematical modeling, system-response analysis, and...
Birkhauser, 1997. — 107 p. DMV Seminar Oberwolfach July 21-27 1996. Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase...
Harvard University, 2019. — 179 p. We discuss in this lecture, what dynamical systems are and where the subject is located within mathematics. The theory of dynamical systems deals with the evolution of systems. It describes processes in motion, tries to predict the future of these systems or processes and understand the limitations of these predictions. All areas of...
Cambridge: Cambridge University Press, 2021. — 229 p. This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many...
Cambridge University Press, 2023. — 509 p. This text, the first of two volumes, provides a comprehensive and self-contained introduction to a wide range of fundamental results from ergodic theory and geometric measure theory. Topics covered include: finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism,...
Cambridge: Cambridge University Press, 2023. — 542 p. The second of two volumes builds on the foundational material on ergodic theory and geometric measure theory provided in Volume I, and applies all the techniques discussed to describe the beautiful and rich dynamics of elliptic functions. The text begins with an introduction to topological dynamics of transcendental...
New York: Springer, 2002. — 428 p. The role of the weak convergence technique via weighted empirical processes has proved to be very useful in advancing the development of the asymptotic theory of the so called robust inference procedures corresponding to non-smooth score functions from linear models to nonlinear dynamic models in the 1990's. This monograph is an ex panded...
New York: Springer, 2020. — 278 p. This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illustrations of their meanings and contents are...
Wiley, 2011. - 386 pages. The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the...
World Scientific, Singapore, 1991. — 185 p. — ISBN 981-02-0587-2. The Carleman linearization has become a new powerful tool in the study of nonlinear dynamical systems. Nevertheless, there is the general lack of familiarity with the Carleman embedding technique among those working in the field of nonlinear models. This book provides a systematic presentation of the Carleman...
Amsterdam: De Gruyter , 2015. - 348p. This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a system are nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds...
Springer, 2012. — 232 p. This book was originally conceived as a continuation in theme of the collec tive monograph Limits of Predictability (Yu. A. Kravtsov, Ed., Springer Series in Synergetics, Vol. 60, Springer-Verlag, Heidelberg, 1993). The main thrust of that book was to examine the various effects and factors (system non stationarity, measurement noise, predictive model...
Berlin: Springer, 1993. — 221 p. Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" by analysing caustics and their fields on the basis of modern catastrophe theory. The present volume covers local and uniform caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions,...
European Mathematical Society, Switzerland, 2012. — 487 p. — (EMS Monographs in Mathematics) — ISBN10: 3037191066 Wave maps are the simplest wave equations taking their values in a Riemannian manifold $(M,g)$. Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric $g$. By Noether's theorem,...
Springer, 1994, — 428 p.
Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. The aim of this volume is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the...
Springer, 2015. — 814 p. — (Applied Mathematical Sciences). — ISBN: 3319123157, 9783319123158. This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students...
Department of Mathematics King’s College London, 2005. — 138 p. General Dynamics . Introduction and Overview. Differential Equations. First Order Autonomous Systems. Second Order Autonomous Systems. Application to Classical Mechanics . Elements of Newtonian Mechanics. Hamiltonian Systems. Lagrangian Theory. Taylor’s Theorem. Basic Linear Algebra.
London: King's College, 2005. — 138 p. The present course is about dynamical systems i.e. systems described by a set of n variables {x1...xn}, each depending on time t, governed by dynamical laws given in terms of ODEs of the form d/ dt xi = fi(t,x1...xn) i = 1...n . (1) We shall learn about methods to analyse such systems. Available methods can generally be classified as (i)...
Chapman & Hall/CRC, 2004. - 360 pages. Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly. The applications of difference equations also grew rapidly, especially with the introduction of graphical-interface software that can plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams,...
(Progress in Systems and Control Theory. Volume 17). New York: Springer Science+Business Media, 1993. – 276 p.
Assembles papers on recent Russian research in these fields, with special emphasis on the treatment of uncertain systems in a deterministic setting. Coverage spans the three main branches of uncertain dynamics – differential games; evolution, estimation and control; and...
Philadelphia: SIAM-Society for Industrial and Applied Mathematics, 2016. — 241 p. Data-driven dynamical systems is a burgeoning field—it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many...
Springer International Publishing, 2021. — 555 p. This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also...
3rd Edition.: Springer, 2004. — 648 p. — (Applied Mathematical Sciences 112). — ISBN 978-1-4419-1951-9. The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense. The idea was to write a simple text that could serve as a seri ous introduction to the subject. Of course,...
4th. ed. — Springer, 2023. — 721 p. — (Applied Mathematical Sciences, 112). — ISBN 3031220064. Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for...
Springer, 2004. — 634 p. — (Applied Mathematical Sciences Volume 112). — ISBN: 978-1-4419-1951-9. This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special...
New York: Springer, 2018. — 366 p. This book focuses on modelling and simulation, control and optimization, signal processing, and forecasting in selected nonlinear dynamical systems, presenting both literature reviews and novel concepts. It develops analytical or numerical approaches, which are simple to use, robust, stable, flexible and universally applicable to the analysis...
Berlin: Springer, 2003. - 627 p. Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences...
N.-Y.: Springer, 2010. - 332p.
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularlysuitable tools for...
Berlin: Springer, 2001. — 400 p. In the present book the modern theory of non-linear oscilla- tions both regular and chaotic, is set out, primarily, as applied to mechanical problems. The material is presented in a non-traditional manner with emphasizing of the new results of the theory otained partially by the author, who is one of the leading experts in the area. Among the...
New York: Springer, 2018. — 267 p. Hybrid System Identification helps readers to build mathematical models of dynamical systems switching between different operating modes, from their experimental observations. It provides an overview of the interaction between system identification, machine learning and pattern recognition fields in explaining and analysing hybrid system...
Springer, 2019. — 298 p. — (Springer Series on Atomic, Optical, and Plasma Physics 109). — ISBN 978-3-030-22651-0. Волноводное распространение нелинейных волн: влияние неоднородности и сопутствующие эффекты This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of...
New York: ITexLi, 2016. — 357 p. This volume is dedicated to nonlinear systems in various fields, and consists of two parts. The book consists mainly of two parts. First. Chapter 1 and Chapter 2 treat design techniques based on linearization of nonlinear systems. An analysis of nonlinear system over quantum mechanics is discussed in Chapter 3. Chapter 4 to Chapter 7 are...
Springer International Publishing AG, 2018. — 561 p. — (Interaction of Mechanics and Mathematics) — ISBN: 978-3-319-56951-2. This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional...
Springer, 2004. — 236 p. — (Lecture Notes in Applied and Computational Mechanics Volume 18). — ISBN: 978-3-642-06029-8. This monograph combines the knowledge of both the field of Nonlinear Dynamcis and Non-smooth Mechanics and presents a framework for a class of non-smooth mechanical systems using techniques from both fields. During the last decades, the Non-smooth Mechanics...
Amsterdam: Springer, 1996. — 414 p. This book is devoted to nonlocal theory of nonlinear oscillations. The frequency methods of investigating problems of cycle existence in multidimensional analogues of Van der Pol equation, in dynamical systems with cylindrical phase space and dynamical systems satisfying Routh-Hurwitz generalized conditions are systematically presented here...
N.-Y.: Springer, 2005. - 300p.
The application of fractals in the engineering sciences is evolving swiftly and the editors have turned to Springer for the third time to bring you the latest research emerging from the rapid growth in techniques available for the employment of the ideas of fractals and complexity to a variety of disciplines in and associated with the engineering...
Amsterdam: Springer, 2011. - 175p.
The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches.
In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst,...
New York: Atlantis Press, 2017. — 190 p. Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of...
New York: Springer, 1992. — 716 p. What's in a name? The original title of our book, Regular and Stochastic Motion, was chosen to emphasize Hamiltonian dynamics and the physical motion of bodies. The new edition is more evenhanded, with considerably more discussion of dissipative systems and dynamics not involving physical motion. To reflect this partial change of emphasis, we...
N.-Y.: Springer, 2015. — 158 p. Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form...
Springer, 2013. — 226 p. — (Springer Series in Synergetics). — ISBN: 3642312500. Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition. The fascinating part is that field...
Cambridge: Cambridge University Press, 2021. — 570 p. Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C^*$-algebras. This Second Edition...
World Scientific Publishing Co. Pte. Ltd.,2009. - 270 pp.
The objective of this book is to review the state-of-the-art chaos control methods for some common nonlinear circuits and systems, such as electronic circuits, power converters, human brains, phase lock loops, sigma delta modulators, etc. and stimulate further research and development in chaos control for nonlinear...
New York: Springer, 1988. — 375 p. In the past several decades many significant results in averaging for systems of ODE's have been obtained. These results have not attracted a tention in proportion to their importance, partly because they have been overshadowed by KAM theory, and partly because they remain widely scattered - and often untranslated - throughout the Russian...
New York: Springer, 2020. — 138 p. This monograph has arisen out of a number of attempts spanning almost five decades to understand how one might examine the evolution of densities in systems whose dynamics are described by differential delay equations. Though the authors have no definitive solution to the problem, they offer this contribution in an attempt to define the...
John Wiley & Sons Ltd, 1997. — 350 p. — (Pure and Applied Mathematics) — ISBN10: 0471967920 This book presents the central issues and emphasizes comparison, assessment and how to combine method and application. It reviews different approaches to guide researchers to appropriate classes of techniques. Includes exercises and solutions and gives an itinerary for readers interested...
Berlin: Springer, 2012. — 220 p. "Pseudochaotic Kicked Oscillators: Renormalization, Symbolic Dynamics, and Transport" presents recent developments in pseudochaos, which is concerned with complex branching behaviors of dynamical systems at the interface between orderly and chaotic motion. Pseudochaos is characterized by the trapping of orbits in the vicinity of self-similar...
Hoboken: Wiley, 2016. — 312 p. Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines...
Springer-Verlag, Berlin, Heidelberg, 2016. – 365 p. – ISBN10: 3662490765 The central theme of this book is the extent to which the structure of the free dynamical boundaries of a system controls the evolution of the system as a whole. Applying three orthogonal types of thinking - mathematical, constructivist and morphological, it illustrates these concepts using applications to...
Springer, 2012. - 507 pages.
This volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the...
3rd edition. — Springer, 2022. — 583 p. — (Springer Series in Synergetics). — ISBN 9783031146404. Нелинейность — это захватывающее проявление наблюдаемой Вселенной, важность которой возрастала на протяжении десятилетий и находила все больше и больше областей применения, начиная от элементарных частиц, ядерной физики, биологии, волновой динамики и т. д. Nonlinearity is a...
De Gruyter, 2015. — 394 p. — (De Gruyter Studies in Mathematical Physics 27). — ISBN: 3110316552. This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in...
Springer, 2020. — 320 p. — (Nonlinear Physical Science). — ISBN: 978-981-15-5211-3. This book focuses on bifurcation and stability in nonlinear discrete systems, including monotonic and oscillatory stability. It presents the local monotonic and oscillatory stability and bifurcation of period-1 fixed-points on a specific eigenvector direction, and discusses the corresponding...
Singapore: Springer, 2020. — 440 p. This is the first book focusing on bifurcation dynamics in 1-dimensional polynomial nonlinear discrete systems. It comprehensively discusses the general mathematical conditions of bifurcations in polynomial nonlinear discrete systems, as well as appearing and switching bifurcations for simple and higher-order singularity period-1 fixed-points...
Springer, 2013. - 239 pp. Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques...
Higher Education Press, Beijing and Springer-Verlag, Berlin, 2010, 386 pages "Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics...
New York: Springer, 2012. - 498 p. Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent...
Springer, 2024. — 240 p. This book is the seventh of 15 related monographs, concerns nonlinear dynamics and singularity of cubic dynamical systems possessing a product-cubic vector field and a self-univariate quadratic vector field. The equilibrium singularity and bifurcation dynamics are discussed. The saddle-source (sink) is the appearing bifurcations for saddle and source...
Springer, 2024. — 245 p. This book is the thirteenth of 15 related monographs on Cubic Dynamical Systems, discusses self- and product-cubic systems with a crossing-linear and self-quadratic products vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed through up-down saddles, third-order concave-source...
Springer-Verlag Berlin Heidelberg 2010. — 311 p. — (Nonlinear Physical Science). — ISBN: 978-3-642-12342-9 (Print) 978-3-642-12343-6 (Online). In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each...
Springer, 2016. — 205 p.
Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes.
Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology. Introduces new concepts, methods, and applications in nonlinear dynamical...
Springer, 2017. — 307 p. — (Nonlinear Systems and Complexity). — ISBN10: 3319427776. This book examines discrete dynamical systems with memory-nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability...
Springer, 2023. — 692 p. — (Nonlinear Physical Science). — ISBN 978-981-16-7872-1. This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical...
Springer, 2021. — 230 p. — (Nonlinear Physical Science). — ISBN 978-981-16-7869-1. The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and...
Springer, 2021. — 452 p. — (Nonlinear Physical Science). — ISBN 978-981-16-7868-4. The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and...
Springer, 2011. — 381 p. — (Nonlinear Physical Science). — ISBN 978-7-04-029710-2. "Complex Systems: Fractionality, Time-delay and Synchronization" covers the most recent developments and advances in the theory and application of complex systems in these areas. Each chapter was written by scientists highly active in the field of complex systems. The book discusses a new...
Basel: Birkhäuser, 2018. — 666 p. — ISBN: 9783319781440, 3319781448. This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary...
World Scientific Publishing, Singapore, 2005, 375 pages, ISBN: 981-256-287-7. This book provides an introduction to a newly developed bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering. The first two chapters of the book contain a brief introduction to the standard bifurcation theory for nonlinear...
Springer, 2019. — 232 p. — (Nonlinear Systems and Complexity 22). — ISBN: 3319785117. This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry...
Springer, 2019. — 232 p. — (Nonlinear Systems and Complexity 22). — ISBN: 3319785117. This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry...
New York: Springer-Verlag, 2011. — 342 p. Nonlinear Dynamics and Complex Systems describes chaos, fractal, and stochasticities within celestial mechanics, financial systems, and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and...
Basel, Switzerland: MDPI, 2014. — 553 p. — ISBN: 978-3-906980-52-2. Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and...
Singapore: World Scientific, 2006. — 363 p. — (World Scientific Series on Nonlinear Science Series A: Volume 58). — ISBN: 9812568174. This book presents a new theory on the transition to dynamical chaos for two-dimensional nonautonomous, and three-dimensional, many-dimensional and infinitely-dimensional autonomous nonlinear dissipative systems of differential equations...
Singapore: World Scientific Publishing Company, 2005. — 448 p. osmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems...
New York: Springer, 2016. - 97 p.
This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which...
Springer, 2016. — 405 p. — (Advances in Delays and Dynamics 04). — ISBN: 978-3-319-18071-7. This volume collects recent advances in nonlinear delay systems, with an emphasis on constructive generalized Lyapunov and predictive approaches that certify stability properties. The book is written by experts in the field and includes two chapters by Miroslav Krstic, to whom this...
Springer, 2012. — 494 p. — (Fields Institute Communications 64). — ISBN: 1461445221. This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential...
New York: CRc Press LLC, 2016. - 338p.
Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors’ new method called...
Springer, 2013. — 608 p. — ISBN10: 1461434742 Advanced Dynamics: Analytical and Numerical Calculations with MatLAB provides a thorough, rigorous presentation of kinematics and dynamics while using MatLAB as an integrated tool to solve problems. Topics presented are explained thoroughly and directly,allowing fundamental principles to emerge through applications from areas such...
Springer, 2012. - 406 pages.
This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called base functions. These are absolutely necessary to obtain the auxiliary functions involved in the...
Springer, 2021. — 479 p. — ISBN 978-3-030-74651-3. This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known...
Springer, 2021. — 479 p. — ISBN 978-3-030-74651-3. This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known...
New York: Springer, 2021. — 476 p. This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic...
New York: John Wiley & Sons Ltd, 1985. — 384 p. In their discussion of the subject of classical mechanics, the authors of this book use a new and stimulating approach which involves looking at dynamical systems from the viewpoint of differential geometry. They discuss the reduction of these systems, and the role played by symmetry and invariance in such reductions. Central to...
New York: Springer, 2009. — 424 p. The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare around 1892 and was extensively discussed by...
New York: Springer, 2014. — 143 p.
The high reliability required in industrial processes has created the necessity of detecting abnormal conditions, called faults, while processes are operating. The term fault generically refers to any type of process degradation, or degradation in equipment performance because of changes in the process's physical characteristics, process...
New York: Springer, 2018. — 196 p. After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering. As with many other approaches to mathematical modeling, the...
Boca Raton: CRC Press/Taylor & Francis Group, 2017. — 228 p.
The investigation of nonlinear systems with a small parameter is attributable by a lot of modern problems of mechanics, physics, hydrodynamics, electrodynamics of charge-particle beams, space technology, astrodynamics and many others. The key problem in solution of various applied problems is that of the stability of...
Singapore: World Scientific, 2018. — 251 p. Modern technological, biological, and socioeconomic systems are extremely complex. The study of such systems largely relies on the concepts of competition and cooperation (synchronization). The main approaches to the study of nonlinear dynamics of complex systems are now associated with models of collective dynamics of networks and...
Cambridge: Cambridge University Press, 2003. — 295 p. — (Cambridge Tracts in Mathematics 148). The main focus of this book is on the development of the theory of Graph Directed Markov Systems. This far-reaching generalization of the theory of conformal iterated systems can be applied in many situations, including the theory of dynamical systems. Dan Mauldin and Mariusz Urbanski...
Cambridge: Cambridge University Press, 2008. — 447 p. The stochastic resonance phenomenon has been observed in many forms of systems and has been debated by scientists for 30 years. Applications incorporating aspects of stochastic resonance have yet to prove revolutionary in fields such as distributed sensor networks, nano-electronics, and biomedical prosthetics. The initial...
2020. — 246 p. These notes address topics in geometry and dynamics, and make contact with some related results in number theory and Lie groups as well. Introduction Ergodic theory Measures and topological dynamics Geometry of the hyperbolic plane Hyperbolic surfaces Arithmetic hyperbolic manifolds Dynamics on hyperbolic surfaces Orbit counting and equidistribution Double cosets...
Cambridge, Cambridge University Press, 2001 - 309 стр.
Statics and dynamics: some elementary concepts.
Review of linear systems.
Stability of fixed points.
Invariant and attracting sets, periodic and quasiperiodic orbits.
Local bifurcations.
Chaotic sets and chaotic attractors.
Characteristic exponents, fractals, homoclinic orbits.
Transition to chaos.
The ergodic...
Cambridge University Press, Cambridge, 2003. — 309 p. — ISBN 0 521 55186. A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic...
Berlin: de Gruyter, 1997. — 328 p. The Verigin problem Review of results Filtration in a porous soil Formulation of the problem Self-similar solutions; Stefan’s problem as a limit case of Verigin’s problem One-dimensional problem: main statements and formulation of results Proofs of Theorems 5.1 and 5.2 : Verigin’s problem with given mass flux on the known boundaries and the...
Taylor & Francis, 2001. — 256 p. This book presents a unified view of mathematical modelling, simulation and control for complex non-linear dynamical systems using soft computing techniques and fractal theory. Our particular point of view is that modelling, simulation and control are problems that can not be considered apart because they are intrinsically related in real-world...
Elsevier, 2016. — 294 p. A Practical Approach to Dynamical Systems for Engineers takes the abstract mathematical concepts behind dynamical systems and applies them to real-world systems, such as a car traveling down the road, the ripples caused by throwing a pebble into a pond, and a clock pendulum swinging back and forth. Many relevant topics are covered, including modeling...
London: Springer-Verlag, 2011. — 340 p. — ISBN: 978-0-85729-611-5; e-ISBN: 978-0-85729-612-2 The goal of this book is to present several concepts useful for the analysis of dynamical systems, and to illustrate, in the last two chapters, how they can be actually applied to improve the state of the art for two classical topics in nonlinear systems theory: the linearization of a...
New York: Springer, 2017. — 386 p. This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. Topics covered include a...
Springer, 2021. — 115 p. This brief presents a suite of computationally efficient methods for bounding trajectories of dynamical systems with multi-dimensional intervals, or ‘boxes’. It explains the importance of bounding trajectories for evaluating the robustness of systems in the face of parametric uncertainty, and for verification or control synthesis problems with respect...
SpringerScience+Business Media, LLC., 2012. XXIX, 1858 p. — ISBN: 978-1-4614-1806-1. Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the...
Leipzig: Max Planck Institute for Mathematics in the Sciences, 2019. — 222 p. This book grew out of the lecture notes for a graduate course we taught during the Summer Semester 2018 at the Max-Planck Institute (MPI) for Mathematics in the Sciences in Leipzig, Germany. Linear algebra is the foundation of much of mathematics, particularly in applied mathematics. Numerical linear...
American Mathematical Society, 2021. — 242 p. — ISBN 978-1470465513. Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and...
Cambridge: Cambridge University Press, 1981. — 238 p. An introductory account of the equations describing nonlinear oscillations and the methods for solving them. This book is concerned primarily with nonlinear oscillations of one dimensional physical systems, which may be represented by the harmonic oscillator equation, with the addition of a “small” nonlinear term. The...
Singapore: World Scientific, 1996. — 332 p. This work is a complete revision of previous book, Introduction to Nonlinear Oscillations (Cambridge University Press, 1981). The earlier book was concerned with the application of various perturbation techniques to the construction of analytic approximations to the oscillatory solutions of second order, nonlinear differential equations....
Springer, 1991. — 140 p. The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group (...
Springer-Verlag New York 2015. — (Applied Mathematical Sciences 193). — 660 pp. — ISBN: 978-1-4939-2705-0 (Print) 978-1-4939-2706-7 (Online).
This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully...
New York, USA: Springer-Verlag, 2015. — 660 pp. — (Applied Mathematical Sciences 193).— ISBN10: 1493927051. This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an...
Princeton: Princeton University Press, 2007. — 284 p. Complexity in Social Worlds. Preliminaries . Modeling. On Emergence. Computational Modeling . Computation as Theory. Why Agent-Based Objects? Models of Complex Adaptive Social Systems . A Basic Framework. Complex Adaptive Social Systems in One Dimension. Social Dynamics. Evolving Automata. Some Fundamentals of Organizational...
Princeton: Van Nostrand Company, 1962. — 732 p. This may be considered as a second (but greatly enlarged) edition of the author’s well-known Introduction to nonlinear mechanics. The field it covers is so vast and complex and has attracted so much attention that, lengthy as the volume is, it contains no more than very brief, but masterly, accounts of many of the topics. The...
Article from magazine: Physica 5D (1982) 370-382.
North-Holland Publishing Company, - 17 стр.
Dynamical systems with quasiperiodic behavior, i.e., two incommensurate frequencies, may be studied via discrete maps which show smooth continuous invariant curves with irrational winding numbers. In this paper these curves are followed using renormalization group techniques which are...
Amsterdam: Springer, 1993. — 290 p. Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations. This volume represents an important contribution to the available methods of solution for such systems. The contents are divided into six chapters....
Springer, 2019. — 239 p. — (Springer Proceedings in Mathematics & Statistics 295). — ISBN: 978-981-32-9831-6. This book is the result of Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation...
Cambridge: Cambridge University Press, 2021. — 449 p. — ISBN 1107151643. Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through...
Cambridge: Cambridge University Press, 2000. — 354 p. Here is a comprehensive introduction to holomorphic dynamics, that is, the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, for example, with the discovery of the Mandelbrot set, and work on chaotic behavior of quadratic maps. The...
ITexLi, 2024. — 136 p. — ISBN 1837691967 9781837691968 1837691959 9781837691951 1837691975 9781837691975. The book examines various practical systems, including models of target detection in cells through the analysis of bio-nanomachine, attractant, and repellent concentrations. It addresses the quasistatic evolution of anelastic structures, explores the generation of...
New York: Springer, 2016. - 199 p. Focuses on the Bond Graph Method, a technique that covers interdisciplinary modeling problems Addresses how to use software, such as MatLAB and Simulink and 20-Sim, to use different modeling paradigms interchangeably Explains all analytical equations with different examples of electrical, mechanical, and mechatronics systems This book...
Springer, 2006. — 249 p. The impact of Bénard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field. The Context of Bénard...
Hindustan Book Agency, India, 2013. — 200 p. — (Texts and Readings in Mathematics 06) — ISBN: 978-93-86279-53-8. The presentation has a slow pace and the book can be read by any person with a background in basic measure theory and metric topology. A new feature of the book is that the basic topics of Ergodic Theory such as the Poincare recurrence lemma, induced automorphisms...
New Delhi: Hindustan Book Agency, 1998. — 228 p. This book treats some basic topics in the spectral theory of dynamical systems, where by a dynamical system we mean a measure space on which a group of automorphisms acts preserving the sets of measure zero. The treatment is at a general level, but even here, two theorems which are not on the surface, one due to H. Helson and W....
2nd Edition. — Springer, 2020. — 223 p. — (Texts and Readings in Mathematics ). — ISBN: 9811562245. This book discusses basic topics in the spectral theory of dynamical systems. It also includes two advanced theorems, one by H. Helson and W. Parry, and another by B. Host. Moreover, Ornstein’s family of mixing rank-one automorphisms is given with construction and proof. Systems...
Singapore: Springer, 2022. — 190 p. Includes select papers presented at the Advanced Instructional School on Ergodic Theory and Dynamical Systems Discusses important and results on ergodic theory and dynamical systems Focuses on applications in areas in number theory and representation theory Real Dynamics Introduction and Preliminaries from Topological Dynamics Preliminaries...
Singapore: Springer, 2023. — 87 p. This book introduces the theory of enveloping semigroups―an important tool in the field of topological dynamics―introduced by Robert Ellis. The book deals with the basic theory of topological dynamics and touches on the advanced concepts of the dynamics of induced systems and their enveloping semigroups. All the chapters in the book are well...
European Mathematical Society, 2011. — 259 p. — (Zurich Lectures in Advanced Mathematics). — ISBN: 3037190957. The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein Gordon and Schr?dinger equations. This is due...
SIAM, 2014. — 231 p. — ISBN: 978-1-611973-33-4. This book introduces key concepts for systematically controlling engineering systems that possess interacting phenomena occurring at widely different speeds. The aim is to present the reader with control techniques that extend the benefits of model reduction of singular perturbation theory to a larger class of nonlinear dynamical...
Wiley-VCH, 1993. — 536 p. Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises.
Wiley-Interscience, 1973. - 425 pages.
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.
New York: Wiley-VCH, 2011. — 342 p. Based on a successful text, this second edition presents different concepts from dynamical systems theory and nonlinear dynamics. The introductory text systematically introduces models and techniques and states the relevant ranges of validity and applicability.New to this edition:3 new chapters dedicated to Maps, Bifurcations of Continuous...
Wiley, 1995. - 720 pages.
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems...
New York: Springer, 2001. — 369 p. Within nonlinear spatio-temporal dynamics, active lattice systems are of relevance to the study of multi-dimensional dynamical systems and the theory of nonlinear waves and dis- sipative structures of extended systems. In this book, the authors deal with basic concepts and models, with methodolo- gies for studying the existence and stability...
American Mathematical Society, 2015. — 120 p. — (MEMOIRS of the American Mathematical Society Vol. 237, No.1122) — ISBN: 1470415445. The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding...
Cambridge University Press, 1995. — 263 p. One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications...
World Scientific, 2007. — 343 p. Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from...
Springer, New York, 1990. — 478 p. — ISBN 0-387-97234-X. This volume deals with controllability and observability properties of nonlinear systems, as well as various ways to obtain input-output representations. The emphasis is on fundamental notions as (controlled) invariant distributions and submanifolds, together with algorithms to compute the required feedbacks.
Boca Raton: CRC Press, 2013. — 322 p. — ISBN-13 978-1-4665-6929-4. The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful...
European Mathematical Society, 2013. — 226 p. — (EMS Tracts in Mathematics 21). — ISBN: 3037191244. In this book dynamical systems are investigated from a geometric viewpoint. Admitting an invariant manifold is a strong geometric property of a dynamical system. This text presents rigorous results on invariant manifolds and gives examples of possible applications. In the first...
New York: Springer, 2017. - 490 p.
This book presents the state-of-the-art in non-linear dynamics and sunspots. These two topics have been the core of an international conference on instability and public policies in a globalized world, organized at Aix-Marseille School of Economics and GREQAM in honor of Jean-Michel Grandmont. He has made significant contributions on general...
Oxford: Oxford University, 2014. - 448 p. The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile...
2nd Edition. — Oxford University Press, 2019. — 493 p. — ISBN 978–0–19–884462–4. The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread...
Springer, 2024. — 456 p. William Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The purpose of the present volume and of the other volumes in the same series is to provide a collection of articles that allows the reader to learn the important aspects of...
World Scientific Publishing, 2018. — 271 p. — (World Scientific Series on Nonlinear Science Series A — Vol. 92). — ISBN: 978-981-3225-28-2. This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original...
Springer, 2020. — 351 p. — ISBN: 978-3-030-37624-6. Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous...
Cham,Springer International Publishing,2020, I Introduction Benchmark Models Variable Structure Systems First- and Higher-Order Sliding Modes Chattering Phenomenon and Discrete-Time Sliding Modes Infinite-Dimensional Sliding Modes Dynamics Under Unilateral Constraints Zhuravlev–Ivanov Transformation Bouncing Ball: State Resets and Zeno Behavior Constrained Van der Pol...
New York: Springer, 2008. - 333p.
Discontinuous Systems develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems, operating under uncertain conditions. While being primarily a research monograph devoted to the theory of discontinuous dynamic systems, no background in discontinuous systems is required;
Berlin: Springer, 2007. — 372 p. The formation of collective behavior in large ensembles or networks of coupled oscillatory elements is one of the oldest and most fundamental aspects of dynamical systems theory. Potential and present applications span a vast spectrum of fields ranging from physics, chemistry, geoscience, through life- and neurosciences to engineering, the...
Cambridge, Cambridge University Press, 1988.
Part I: Classical dynamics.
Linear dynamics systems.
Nonlinear systems.
Chaotic motion.
Normal forms.
Maps of the cycle.
Integrable and quasi-integrable systems.
Part II: Quantum dynamycs.
Torus quantization.
Quantization of ergodic systems.
Periodic orbits in quantum mechanics.
Springer, 2013. — XVI, 356 p. — (Computational Methods in Applied Sciences Volume 26) — ISBN: 978-94-007-5133-0, ISBN: 978-94-007-5134-7 (eBook). The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification...
Springer, 2011. — 342 p.
At the dawn of the 21st century, computational stochastic dynamics is an emerging research frontier. This book focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The book is primarily intended for researchers and post-graduate...
Springer, 2019. — 350 p. — ISBN: 9811392536. This book presents up-to-date research developments and novel methodologies to solve various stability and control problems of dynamic systems with time delays. First, it provides the new introduction of integral and summation inequalities for stability analysis of nominal time-delay systems in continuous and discrete time domain,...
W.A. Benjamin, Inc., 1969. — 140 p. These notes are based on lectures given during the autumn of 1966 at Yale University. Ten years ago Kolmogorov introduced entropy into ergodic theory and solved an important classification problem in this subject. Since then entropy theory has been extensively refined and applied to a variety of old and new problems. I have had to limit...
New York: AMS, 2009. - 334p.
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets,...
University Of Chicago Press, 1998. — 318 p. The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable...
Cambridge University Press, 1995. — 445 p. Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence,...
Springer, 2011. - 218 pages. "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by MatLAB programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution...
Springer International Publishing AG, 2018. — 497 p. — (Studies in Systems, Decision and Control 133). — ISBN: 331971242X. This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with...
Springer International Publishing AG, 2018. — 497 p. — (Studies in Systems, Decision and Control 133). — ISBN: 331971242X. This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with...
Springer, 2017. — 111 p. — (SpringerBriefs in Applied Sciences and Technology). — ISBN 978-3-319-53720-7. This brief provides a general overview of nonlinear systems that exhibit hidden-attractor behavior, a topic of interest in subjects as divers as physics, mechanics, electronics and secure communications. The brief is intended for readers who want to understand the concepts...
Amsterdam: Springer, 2003. — 257 p. Synchronization is a universal phenomenon that is encountered in nature, science and engineering. The book presents a broad view of modern theoretical and experimental approaches to synchronization, especially in complex and chaotic systems, and its applications in life sciences and engineering. Contributors include applied mathematicians,...
Cambridge University Press, 2001. — 433 p. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae,...
Springer, 2023. — 461 p. This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford’s algebras, give rise to the essentially nonlinear...
Springer, 2010. — ISBN10: 3642127983; ISBN13: 978-3642127984. Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of unusual physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of...
Springer International Publishing AG, 2017. — 228 p. — (Lecture Notes in Mathematics 2193) — ISBN: 978-3-319-65183-5. Provides a survey of current research and new approaches in the theory of shadowing of approximate trajectories of dynamical systems see more benefits Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this...
2nd Rev. and Exten. Edition. — De Gruyter, 2019. — 260 p. — ISBN: 978-3-11-065716-6. The second edition of this book is an expanded and corrected variant of its first edition published by Walter De Gruyter, Berlin/Boston in 2012 in the series “Studies in Mathematical Physics,” Vol. 3. This edition contains a new chapter, Chapter 13, on invariant measures, in which we describe...
Springer, 2019. — 136 p. This book presents a new approach for the analysis of chaotic behavior in non-linear dynamical systems, in which output can be represented in quaternion parametrization. It offers a new family of methods for the analysis of chaos in the quaternion domain along with extensive numerical experiments performed on human motion data and artificial data. All...
Springer Series in Synergetics. Springer-Verlag, Berlin-Heidelberg, 2006, 369 p.
Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium is a paradigmatic case of emergent behaviour associated with complex systems. It is encountered in a great variety of settings, both in nature and technology, and has numerous applications ranging from nonlinear...
Plakhov A.
Springer New York Heidelberg Dordrecht London. 2012. — 284 pages.
Notation and Synopsis of Main Results
Problem of Minimum Resistance to Translational Motion of Bodies
Newton’s Problem in Media with Positive Temperature
Scattering in Billiards
Problems of Optimal Mass Transportation
Problems on Optimization of Mean Resistance
The Magnus Effect and the Dynamics...
Cambridge: Cambridge University Press, 1993. - 171 p. Pesin theory consists of the study of the theory of non-uniformly hyperbolic diffeomorphisms. The aim of this book is to provide the reader with a straightforward account of this theory, following the approaches of Katok and Newhouse. Emphasis is placed on generality and on the crucial role of measure theory, although no...
Chаm: Springer International Publishing, 2017. — 207 p. The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by...
Cambridge: Cambridge University Press, 1998. — 194 p. This book is an introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. The authors provide a number of applications, principally to number theory and...
Birkhäuser Basel, 2014. — 310 p. The exposition in the book begins with the consideration of the key elements lying at the foundation of Lobachevsky’s geometry, including its interpretations (models), and is carried out in a form adapted to the methods of modern geometry, function theory, and the theory of nonlinear differential equations. The central part of the book is...
Berlin: Springer, 2010. — 430 p. Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional...
North-Holand, 2000 - 107 стр. Quantization of the 3D Sinai billiard. Quantal spectral statistics. Classical periodic orbits. Semiclassical analysis. The accuracy of the semiclassical energy spectrum. Semiclassical theory of spectral statistics.
Spain, Springer, 1997 - 202 стр.
Saddle-Focus Connections.
The Unimodal Family.
Contractive Directions.
Critical Points of the Bidimensional Map.
The Inductive Process.
The Binding Point.
The Binding Period.
The Exclusion of Parameters.
Beijing: Springer, Kluwer Academic Publishers, 2001. -402p
Nonlinear Control Systems and Power System Dynamics presents a comprehensive description of nonlinear control of electric power systems using nonlinear control theory, which is developed by the differential geometric approach and nonlinear robust control method. This book explains in detail the concepts, theorems and...
2nd Edition. — Springer, 2015. — 315 p. — ISBN: 978-3-319-21872-4. The presentation of the theory is made using the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The corresponding global existence theorems have been proved mainly in the last decade, focussing on fully nonlinear systems. Related questions...
New York: Wiley-VCH, 2004. — 606 p. This reference work provides a comprehensive insight into past developments in the application of non–linear dynamics, such as production systems in the manufacturing and process engineering, mechanical engineering and plant construction and automation technology.
New York: Wiley, 1990. — 242 p. — ISBN 0-471-63418-2. Written when the young science of chaos was gaining a foothold in the scientific community, this book introduces the field's concepts, applications, theory, and technique. Suitable for advanced undergraduates and graduate students, researchers, and teachers of mathematics, physics, and engineering, the text's major...
Berlin: Springer, 2007. — 225 p. Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity...
Springer, 2019. — 135 p. — (Springer Theses). — ISBN 978-3-030-18235-9. Неравновесная динамика за пределами дефазирования Cold atomic gases trapped and manipulated on atom chips allow the realization of seminal one-dimensional (1d) quantum many-body problems in an isolated and well controlled environment. In this context, this thesis presents an extensive experimental study of...
Springer, 1991. - 178 Pages.
Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions...
Boca Raton: CRC Press, 1998. — 522 p. Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student focusing on...
Cambridge: Cambridge University Press, 2011. — 219 p. This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering...
Boca Raton: CRC Press, 2021. — 119 p. For almost every phenomenon in physics, chemistry, biology, medicine, economics, and other sciences, one can make a mathematical model that can be regarded as a dynamical system. One-Dimensional Dynamical Systems: An Example-Led Approach seeks to deep-dive into α standard maps as an example-driven way of explaining the modern theory of the...
Wiley, 2008. — 112 p. If you are a student of Engineering (any branch), B.Sc./M.Sc., or Business Management, then this book is for you. It will expose you to a subject evolved at Massacheusettes Institute of Technology, Boston, initiated by the inventor of random access magnetic core memory Germeshausen Professor Jay W. Forrester and demonstrates how to apply the subject into...
Singapore: World Scientific, 2017. — 194 p. The Geometric Theory of Foliations is one of the fields in Mathematics that gathers several distinct domains: Topology, Dynamical Systems, Differential Topology and Geometry, among others. Its great development has allowed a better comprehension of several phenomena of mathematical and physical nature. Our book contains material...
CRC Press, 2019. — 248 p. This book is devoted to the study of nonlinear evolution and difference equations of first and second order governed by a maximal monotone operator. This class of abstract evolution equations contains not only a class of ordinary differential equations, but also unify some important partial differential equations, such as the heat equation, wave...
Bristol: IOP Publishing, 2019. — 190 p. This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, MatLAB (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded...
Berlin: Springer-Verlag, 2013. — 781 p. Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the...
Academic Press, 1989. - 187 Pages.
The study of differentiate dynamical systems — differentiate dynamics — has been one of the most successful fields of mathematical research in the last twenty years. Many profound results have been uncovered and applied to other branches of mathematics as well as to the natural sciences. The explosive development of the subject has...
Chapman and Hall, 2000. — 315 p. Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out. Self-Similarity and Beyond presents a myriad...
Springer, 1986. — 269 p. Proceedings of a Workshop Held at the Naval Surface Weapons Center, Silver Spring, MD, July 23–26, 1984. Global aspects of periodic solutions of nonlinear conservative system M. S. Berger Lecture 1: On resonant hamiltonian systems with finitely many degrees of freedom. Martin Kummer Lecture 2: Realizations of the reduced phase space of a hamiltonian...
CRC Press, 2021. — 218 p. — ISBN 978-1-032-02568-1. Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an...
Berlin: VDM Verlag Dr. Müller, 2010. - 654p.
Differential and difference equations have long played important roles in the history of theoretical models. The oscillation theory as a part of the qualitative theory of these types of equations has been developed rapidly in the past thirty years. The extensive application prospect facilitates the development of this field. Our...
Saarbrucken: Lambert Academic Publishing, 2010. — 587 p. The study of dynamic equations on time scales, which goes back to its founder Stefan Hilger is an area of mathematics and has been created in order to unify the study of differential and difference equations. The oscillation theory as a part of the qualitative theory of dynamic equations on time scales has been developed...
Boston: Kluwer Academic Publishers, 2004. — 318 p. Averaging Method in Oscillation Systems with Variable Frequencies Aceraging Method in Multipoint Problems Integral Manifolds Investigation of a Dynamical System in a Neighborhood of a Quasiperiodic Trajectory back-matter
2nd Edition. — New York: Springer, 2007. — 444 p. — ISBN 978-0-387-48916-2. Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of...
Osnabrück: Der Andere Verlag, 2000. — 176 p. — ISBN 3-934366-76-7. Differential geometry in Mathematica Germs of functions Jets R-equivalence Local behaviour of smooth maps Unfoldings The Seven Elementary Catastrophes Shock Waves
Springer, 2020. — 94 p. — (BestMasters). — ISBN: 978-3-658-29110-5. In this book, Paulo Guilherme Santos studies diagonalization in formal mathematics from logical aspects to everyday mathematics. He starts with a study of the diagonalization lemma and its relation to the strong diagonalization lemma. After that, Yablo’s paradox is examined, and a self-referential...
Springer, 1999. - 704 pages. There has been a great deal of excitement over the last few years concerning the emergence of new mathematical techniques for the analysis and control of nonlinear systems: witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos and other complicated dynamical behaviour and the development of a comprehensive theory...
1st edition. — Cambridge: Cambridge University Press, 1980. — 144 p. — ISBN 0521297826. Almost every scientist has heard of catastrophe theory and knows that there has been a considerable amount of controversy surrounding it. Yet comparatively few know anything more about it than they may have read in an article written for the general public. The aim of this book is to make it...
2000. — 289 p. — ISBN: 0-13-185000-8. This is the internet version of Invitation to Dynamical Systems. Unfortunately, the original publisher has let this book go out of print. The version you are now reading is pretty close to the original version (some formatting has changed, so page numbers are unlikely to be the same, and the fonts are different). Popular treatments of...
World Scientific, 2007. - 453 p. - Nonlinear dynamics of complex processes is an active research field with large numbers of publications in basic research, and broad applications from diverse fields of science. Nonlinear dynamics as manifested by deterministic and stochastic evolution models of complex behavior has entered statistical physics, physical chemistry, biophysics,...
A K Peters, 2009. — 600 p. Complex Dynamics: Families and Friends features contributions by many of the leading mathematicians in the field, such as Mikhail Lyubich, John Milnor, Mitsuhiro Shishikura, and William Thurston. Some of the chapters, including an introduction by Thurston to the general subject of complex dynamics, are classic manuscripts that were never published...
Cambridge: Cambridge University Press, 2016. — 230 p. Multi-scale systems, involving complex interacting processes that occur over a range of temporal and spatial scales, are present in a broad range of disciplines. Several methodologies exist to retrieve this multi-scale information from a given time series; however, each method has its own limitations. This book presents the...
N.-Y.: Wiley-VCH, 2007. - 852p. This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions...
Wiley, 2008. - 229 p. Adopting a cross–disciplinary approach, the review character of this monograph sets it apart from specialized journals. The editor is advised by a first–class board of international scientists, such that the carefully selected and invited contributions represent the latest and most relevant findings. The resulting review enables both researchers and...
Wiley, 2010. - 262 p. Written in a style that breaks the barriers between the disciplines, this monograph enables researchers from life science, physics, engineering, or chemistry to access the most recent results in a common language. The resulting review character of this project sets it apart from specialized journals, and allows each volume to respond quickly to new...
Wiley-VCH, 2009. - 258 pages.
Adopting a cross–disciplinary approach, the review character of this monograph sets it apart from specialized journals. The editor is advised by a first–class board of international scientists, such that the carefully selected and invited contributions represent the latest and most relevant findings. The resulting review uses a common language and...
Princeton: Princeton University Press, 2009. — 321 p. Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks...
Berlin: Springer-Verlag. - 2007. - 370 p. (The Frontiers collection) It has been suggested that the big questions of science are answered – that science has entered a "twilight age" where all the important knowledge is known and only the details need mopping up. And yet, the unprecedented progress in science and technology in the twentieth century has raised questions that...
ITexLi, 2023. — 153 p. — ISBN 1803565675 9781803565675 1803565667 9781803565668 1803565683 9781803565682. It is well known that the theory of dynamical systems is an essential mathematical tool in the analysis of various real-world processes and phenomena that evolve over time. Different aspects of this rich field of research are evolving all the time, including new theoretical...
London: Springer, 2011. - 284p. Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability. Stability conditions for difference equations with delay can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability...
New York: Springer, 2017. — 136 p. This thesis develops several systematic and unified approaches for analyzing dynamic systems with positive characteristics or a more general cone invariance property. Based on these analysis results, it uses linear programming tools to address static output feedback synthesis problems with a focus on optimal gain performances. Owing to their...
Singapore: World Scientific Publishing Company, 2014. — 258 p. This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering,...
2nd edition. — Springer, 2023. — 683 p. This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens...
New York: Springer, 2007. — 518 p. This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial...
Springer. Second, Expanded and Revised Edition.
General Ergodic Theory of Groups of Measure Preserving Transformations, Ergodic Theory of Smooth Dynamical Systems, Dynamical Systems on Homogeneous Spaces, The Dynamics of Billiard Flows in Rational Polygons, Dynamical Systems of Statistical Mechanics and Kinetic Equations.
CRC Press, 2015. - 304 pp. Excitable media comprise a class of models for a wide range of physical, chemical, and biological systems that exhibit spontaneous formation of spatial patterns. Patterns in Excitable Media: Genesis, Dynamics, and Control explores several aspects of the dynamics of such patterns—in particular their evolution upon interaction with structural and...
L.: Anthem Press, 2006. - 323p. An attempt to familiarize the reader with nonlinear systems, in particular qualitative characteristics in a variety of systems amenable to mathematization. Preamble Motivation Recapturing linear ordinary differential equations Linear systems : qualitative behaviour Stability studies Study of equilibria : another approach Non-linear vis a vis...
Boca Raton: CRC Press, 2021. — 404 p. Dedicated to Professor S. Leela in recognition of her significant contribution to the field of nonlinear dynamics and differential equations, this text consists of 38 papers contributed by experts from 15 countries, together with a survey of Professor Leela's work. The first group of papers examines stability, the second process controls,...
Springer-Verlag Berlin Heidelberg, 2008. — 383 p. — (Lecture Notes in Physics 730). — ISBN: 978-3-540-72997-6 (eBook), 978-3-642-09210-7 (Softcover), 978-3-540-72996-9 (Hardcover). For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. The aim of this book is to give a systematic introduction to and overview...
Springer, 2023. — 145 p. — (SpringerBriefs on PDEs and Data Science). — ISBN 978-981-19-6817-4. This book introduces an interesting and alternative way to design absorbing boundary conditions (ABCs) for quantum wave equations, basically the nonlinear Schrödinger equation. The focus of this book is the application of the phase space filter approach to derive accurate radiation...
Singapore: World Scientific Publishing, 2022. — 325 p. A recent development is the discovery that simple systems of equations can have chaotic solutions in which small changes in initial conditions have a large effect on the outcome, rendering the corresponding experiments effectively irreproducible and unpredictable. An earlier book in this sequence, Elegant Chaos:...
Basel: Birkhäuser, 2008. — 435 p. Differential equations are a fast evolving branch of mathematics and one of the mathematical tools most used by scientists and engineers. This book gathers a collection of original articles and state-of-the-art contributions, written by highly distinguished researchers working in differential equations, delay-differential equations,...
World Scientific Publishing Co. Pte. Ltd., 2017. — 302 p. — (Analysis, Applications and Computation. Volume 7) — ISBN10: 9814678295 This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of "recursive" hyperbolic functions based on the...
Singapore: World Scientific Publishing, 1993. — 180 p. — ISBN: 981-02-1355-7 Простое введение в теорию точечных преобразований, с приложениями к проблеме интегрируемости нелинейных дифференциальных и разностных уравнений. First-order ordinary differential equation Second-order ordinary differential equations Second-order ordinary differential equation Systems of second-order...
Singapore, World Scientific Publishing, 2005. - 607 p.
Книга посвящена вопросам нелинейной и хаотической динамики, включая фракталы, вейвлеты, клеточные автоматы, нейросети, скрытые марковские процессы, нечёткую логику и т.п.
World Scientific Publishing Company, 1999. - 585 pages.
This book is an overview of all of the components of nonlinear dynamics. Nonlinear dynamics is a field of study that enables well-constructed predictive modeling of systems that might be difficult to solve otherwise. Such continuous systems were first widely modeled by ordinary and differential equations, but with the...
World Scientific, 2001. — 596 p. The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail. The numerical and symbolic methods are implemented in C++, SymbolicC++...
6th Edition. — World Scientific, 2015. — 682 p. — ISBN: 9814583472. The Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, more than 100 worked...
6th ed. — Singapore: World Scientific Publishing Company, 2014. — 682 p. — ISBN 9814583472. The Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material,...
Singapore: World Scientific, 2005. - 607p.
The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail. The numerical and symbolic methods are implemented in C++,...
Singapore: World Scientific Publishing Company, 2009. - 225p. This book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology, communication or laser physics. Over the last decade, new types...
Volume II. — Princeton University Press, 2003. — 398 p. Fourier Analysis: An Introduction. Complex Analysis. Real Analysis. Measure Theory, Integration, and Hilbert Spaces.
Society for Industrial & Applied Mathematics, 2011. — 387 p. This is the only book that comprehensively addresses dynamics with inequalities. The author develops the theory and application of dynamical systems that incorporate some kind of hard inequality constraint, such as mechanical systems with impact; electrical circuits with diodes (as diodes permit current flow in only...
2nd edition. — Boca Raton: CRC Press, 2018. — 519 p. Chaos, Fractals, and Dynamics Capsule History of Dynamics The Importance of Being Nonlinear A Dynamical View of the World 1D Flows A Geometric Way of Thinking Fixed Points and Stability Population Growth Linear Stability Analysis Existence and Uniqueness Impossibility of Oscillations Potentials Solving Equations on the...
Perseus Books Publishing, 2000. — 516 p. — ISBN: 0-7382-0453-6. This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their...
New York: Westview Press, 2001. - 505p.
An introductory text in nonlinear dynamics and chaos, emphasizing applications in several areas of science, which include vibrations, biological rhythms, insect outbreaks, and genetic control systems. Contains a rich selection of illustrations, with many exercises and examples.
Boca Raton: Westview Press, 2016. — 404 p. This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the second edition of Steven Strogatz's classic textNonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.The textbook and accompanying Student Solutions Manual are aimed at newcomers to nonlinear...
New York: Springer, 2012. — 297 p. — ISBN 978-1-4614-3127-5. Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of...
Wiley, 1985. — 388 p. Discusses the theoretical aspects and results of smooth dynamical systems. Covers dynamical systems on manifolds of one or two dimensions, generic properties, stability theory, invariant measures for differentiable dynamical systems, and topological entrophy. Contains definitions and exercises for problem-solving practice.
New York: Springer, 1996. — 221 p. In 1992 two successive symposia were held in Japan on algorithms, fractals and dynamical systems. The first one was Hayashibara Forum '92: International Symposium on New Bases for Engineering Science, Algorithms, Dynamics and Fractals held at Fujisaki Institute of Hayashibara Biochemical Laboratories, Inc. in Okayama during November 23-28 in...
Cambridge University Press, 2014. - 511 pp. Introducing a unified framework for describing and understanding complex interacting systems common in physics, chemistry, biology, ecology, and the social sciences, this comprehensive overview of dynamic critical phenomena covers the description of systems at thermal equilibrium, quantum systems, and non-equilibrium systems. This...
Springer, 2010. - 434 pages.
This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include: Chaotic Dynamics and Transport in...
Springer International Publishing AG, 2017. — 184 p. — (Springer Theses) — ISBN: 9783319-529493 Fractional-order calculus offers a novelmodeling approach for systems with extraordinary dynamical properties by introducing the notion of a derivative of noninteger (fractional) order. During the last 300 years fractional-order calculus has been the subject of moderately active...
Springer Cham Heidelberg New York Dordrecht London, 2014. VIII, 368 p. 162 illus. — (Computational Methods in Applied Sciences, Vol. 35).
Contributions by the most distinguished researchers in the field
Coverage of the most relevant scientific topics in the field
High-level scientific quality
By having its origin in analytical and continuum mechanics, as well as in...
Springer, 2024. — 200 p. The main challenge in the study of nonautonomous phenomena is to understand the very complicated dynamical behaviour both as a scientific and mathematical problem. The theory of nonautonomous dynamical systems has experienced a renewed and steadily growing interest in the last twenty years, stimulated also by synergetic effects of disciplines which have...
Oxford University Press, 2018. — 444 p. This book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it ecosystems, societies, traffic, financial markets, opinion formation and spreading, or the internet and social media. Complex systems are...
Springer, 2025. — 368 p. — ISBN-13 978-3031773778 This book presents Analytical and Approximate Methods for Complex Dynamical Systems and introduces ideas of discontinuous mapping treated as complex dynamical systems. Mathematicians of world-recognized Ukrainian scientific schools established by M.Krylov, M.Bogolyubov, Yu.Mitropolskiy, and A.Sharkovsky used to cooperate for...
N.-Y.: Springer, 2015. -361p.
This book presents recent advances, new ideas and novel techniques related to the field of nonlinear dynamics, including localized pattern formation, self-organization and chaos. Various natural systems ranging from nonlinear optics to mechanics, fluids and magnetic are considered. The aim of this book is to gather specialists from these various...
Springer, 2016. - 298 pp. The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with...
Morgan & Claypool, 2018. — 185 p. The Boussinesq equation is the first model of surface waves in shallow water that considers the nonlinearity and the dispersion and their interaction as a reason for wave stability known as the Boussinesq paradigm. This balance bears solitary waves that behave like quasi-particles. At present, there are some Boussinesq-like equations. The...
Springer-Verlag Berlin, 2010, 298 pages Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The...
Singapore: World Scientific Publishing Company, 1987. — 177 p. This book is an exposition on the interesting interplay between topological dynamics and the theory of C*-algebras. Researchers working in topological dynamics from various fields in mathematics are becoming more and more interested in this kind of algebraic approach of dynamics. This book is designed to present to...
New York: Springer, 2019. — 172 p. The interplay between synchronization and spatio-temporal pattern formation is central for a broad variety of phenomena in nature, such as the coordinated contraction of heart tissue, associative memory and learning in neural networks, and pathological synchronization during Parkinson disease or epilepsy. In this thesis, three open puzzles of...
Springer, 2019. — 405 p. — ISBN: 978-3-030-02588-5. This book explores the interdisciplinary field of complex systems theory. By the end of the book, readers will be able to understand terminology that is used in complex systems and how they are related to one another; see the patterns of complex systems in practical examples; map current topics, in a variety of fields, to...
Hoboken: CRC Press, 2013. — 363 p. Authors Introduction to Mathematical Modeling Modeling of Systems from Natural Science Introduction to Chaotic Dynamics Chaotic Dynamics in Model Systems from Natural Science Modeling of Some Engineering Systems Solutions to Odd-Numbered Problems
CRC Press; Taylor & Francis Group, 2014. — 363p. — ISBN13: 978-1-4398-9887-1. Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MatLAB. The book first covers the necessary mathematical preliminaries, including testing of stability. It then...
Berlin: de Gruyter, 2022. — 524 p. The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric...
De Gruyter, 2023. — 440 p. Complex dynamics is one of the most fascinating subjects of study and research in mathematics. This third volume in the series entitled Non-Invertible Dynamical Systems not only examines topological and analytical properties of the iteration of rational functions on the Riemann sphere (in particular, the Fatou and Julia sets) but also focuses on...
Berlin: ds Gruyter, 2021. — 458 p. Preface List of Figures Introduction to Volume 1 Dynamical systems Homeomorphisms of the circle Symbolic dynamics Distance expanding maps (Positively) expansive maps Shub expanding endomorphisms Topological entropy Ergodic theory Measure-theoretic entropy Infinite invariant measures Topological pressure The variational principle and...
Nova Science Publishers, Inc., 2017. — 576 p. — (Theoretical and Applied Mathematics). — ISBN10: 1536120324, 13 978-1536120325. The book has two volumes and consists of forty-four chapters, which are divided into five sections: Mathematical treatment of non-linear problems, including the differential equations, numerical methods, algorithms and solutions; theoretical and...
Nova Science Publishers, Inc., 2017. — 374 p. — (Theoretical and Applied Mathematics). — ISBN10: 1536121630, 13 978-1536121636. The book has two volumes and consists of forty-four chapters, which are divided into five sections: Mathematical treatment of non-linear problems, including the differential equations, numerical methods, algorithms and solutions; theoretical and...
Berlin: de Gruyter, 2013. — 316 p. This book focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The...
Springer International Publishing AG, 2017. — 145 p. — (Springer Series in Synergetics) — ISBN: 978-3-319-51892-3 This book is primarily concerned with the computational aspects of predictability of dynamical systems – in particular those where observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for...
2nd Edition. — Springer, 2019. —207 p. — (Springer Series in Synergetics). — ISBN: 978-3-030-28629-3. This book is primarily concerned with the computational aspects of predictability of dynamical systems - in particular those where observations, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, in astronomy it is...
London: Academic Press, 2020. — 311 p. Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industrial contexts to help readers understand and use this innovative algorithm. Data-driven modelling of complex systems is a rapidly evolving field, which has applications in...
Cambridge: Cambridge University Press, 2014. - 213p.
The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the...
Cambridge: Cambridge University Press, 2016. — 556 p. Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete...
New York: Springer, 2021. — 204 p. This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges,...
Springer, 2021. — 210 p. — ISBN 978-981-16-2852-8. This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namely Entropy, information, and complexity functions Multistability, oscillations, and rhythmic synchronization Diffusions, rotation, and convection in fluids The collection of works devoted...
Springer, 2021. — 210 p. — ISBN 978-981-16-2852-8. This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namely Entropy, information, and complexity functions Multistability, oscillations, and rhythmic synchronization Diffusions, rotation, and convection in fluids The collection of works devoted...
Basel: MDPI AG, 2019. — 292 p. In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors...
Berlin: De Gruyter, 2014. — 515 p. There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate...
2nd Edition. — American Mathematical Society, 1999. — 315 p. — ISBN: 0821809423. The publication of this book in 1970 marked the culmination of a particularly exciting period in the history of the topology of manifolds. The world of high-dimensional manifolds had been opened up to the classification methods of algebraic topology by Thom's work in 1952 on transversality and...
Springer, 2000. — 251 p. This text provides an introduction to ergodic theory suitable for readers knowing basic measure theory. The mathematical prerequisites are summarized in Chapter 0. It is hoped the reader will be ready to tackle research papers after reading the book. The first part of the text is concerned with measure-preserving transformations of probability spaces;...
Springer, 2022. — 195 p. — (Synthesis Lectures on Mathematics & Statistics). — ISBN 978-3-031-11235-5. Динамические уравнения и почти периодические нечеткие функции на шкалах времени This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a...
European Mathematical Society, 2009. — 773 p. — (IRMA Lectures in Mathematics and Theoretical Physics 14). — ISBN 978-3-03719-546-8. This book presents in a concise and accessible way, as well as in a common setting, various tools and methods arising from spectral theory, ergodic theory and stochastic processes theory, which form the basis of and contribute interactively a...
Philadelphia: American Mathematical Society, 2016. — 205 p. This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the...
Singapore: World Scientific, 2000. — 462 p. General model of system with discontinuities Systems with clearances Systems with piecewise variable stiffness Impacting systems Systems with dry friction Systems with multi-mode discontinuities Smoothing discontinuities Discussion.
Springer, 2003. — 860 p. This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He...
Second Edition. — Springer, Switzerland, 2022. — 270 p. — ISBN 978-3-031-01248-8. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. This second edition includes additional material and in particular a new chapter on...
Springer International Publishing, 2014. — 206 p. — (Graduate Texts in Physics). — ISBN: 978-3-319-06343-0, 978-3-319-06342-3. The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos,...
Springer International Publishing Switzerland, 2016. – 329 p. – ISBN10: 3319263676. This book mostly results from a selection of papers presented during the 11th IFAC (International Federation of Automatic Control) Workshop on Time-Delay Systems, which took place in Grenoble, France, February 4 - 6, 2013. During this event, 37 papers were presented. Taking into account the...
Elsevier, 2005. — 321 p. Molecular vibration Concepts of dynamical groups Concepts of nonlinear dynamics Application of su(2) algebra Application of noncompact su(1,1) algebra Breaking of su(3) algebra and its application Application of su(3) algebra Quantal effect of asymmetric molecular rotation Pendulum, resonance and molecular highly excited vibration Quasiperiodicity,...
Springer International Publishing AG, 2017. — 257 p. — ISBN: 3319582852. This monograph summarizes the recent major achievements in Möbius invariant Qk spaces. First introduced by Hasi Wulan and his collaborators, the theory of Qk spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers...
World Scientific, 2023. — 381 p. There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an...
Morgan & Claypool Publishers, 2021. — 89 p. — (Synthesis Lectures on Mechanical Engineering). — ISBN 978-1681739441. In this book, the global sequential scenario of bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is presented for a better understanding of global behaviors and motion transitions for one periodic motion to another one. A...
ITexLi, 2023. — 222 p. — ISBN 1803569271 9781803569277 1803569263 9781803569260 180356928X 9781803569284. In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of input. Nonlinear control systems, which are among the new technologies most widely used in many fields such as economic management, industrial...
De Gruyter, 2014. — 389 p. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's...
Springer, 2010. - 218 p. - This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the...
Springer, 1997. — 555 p. This book deals with predictability and dynamical concepts in biology and physics. The main emphasis is on intrinsic stochasticity caused by the instability of dynamical equations. In particular, the authors present for the first time in book form their concept of terminal dynamics. They demonstrate that instability as an attribute of dynamical models can...
Springer, 2018. — 135 p. — (Lecture Notes in Mathematics 2214). — ISBN: 3319788094. This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and...
Berlin, Heidelberg, New York, London: Springer-Verlag, 1991. — XIV, 321 p. — Springer Series in Nonlinear Dynamics. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real classical or quantum systems....
Berlin: Springer, 1991. — 338 p. The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E.D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with...
New York: Springer, 2010. — 267 p. A number of optimization problems of the mechanics of space flight and the motion of walking robots and manipulators, and of quantum physics, eco momics and biology, have an irregular structure: classical variational proce dures do not formally make it possible to find optimal controls that, as we explain, have an impulse character. This and...
European Mathematical Society, 2010. — 363 p. This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure...
Springer, 2014. - 292 p. - This book is based on the outcome of the 2012 Interdisciplinary Symposium on Complex Systems held at the island of Kos. The book consists of 12 selected papers of the symposium starting with a comprehensive overview and classification of complexity problems, continuing by chapters about complexity, its observation, modeling and its applications to...
Springer-Verlag Berlin Heidelberg, 2013. — 283 p. — ISBN 978-3-642-33227-2. This proceeding book of Nostradamus conference contains accepted papers presented at this event in 2012. Nostradamus conference was held in the one of the biggest and historic city of Ostrava (the Czech Republic, in September 2012. Conference topics are focused on classical as well as modern methods for...
CRC Press, 2019. — 402 p. Review of Chaotic Dynamics. Human Immunodeficiency Virus and Urbanization Dynamics. Chaotic Behaviors in Piecewise Linear Mappings. Robust Chaos in Neural Networks Models. Estimating Lyapunov Exponents of 2-D Discrete Mappings. Control, Synchronization and Chaotification of Dynamical Systems. Boundedness of Some Forms of Quadratic Systems. Some Forms...
World Scientific Publishing Company, 2011. - 268 pages. This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of...
Singapore: World Scientific, 2010. — 357 p. This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the H?non map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps,...
Springer, 2021. — 323 p. — (Studies in Systems, Decision and Control, 353). — ISBN 978-3030685997. This book deals with the stabilization issue of infinite dimensional dynamical systems both at the theoretical and applications levels. Systems theory is a branch of applied mathematics, which is interdisciplinary and develops activities in fundamental research which are at the...
Springer, 2021. — 323 p. — (Studies in Systems, Decision and Control, 353). — ISBN 978-3030685997. This book deals with the stabilization issue of infinite dimensional dynamical systems both at the theoretical and applications levels. Systems theory is a branch of applied mathematics, which is interdisciplinary and develops activities in fundamental research which are at the...
New York: Springer, 2017. — 240 p. Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and...
Springer, 2018. — 265 p. Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: constructive existence results and regularity theorems for all weak solutions; convergence results for solutions and their...
Springer, 2020. — 226 p. — (Communications and Control Engineering). — ISBN 13 9783030259723. Динамические системы с дискретным временем и дискретным пространством Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of The book's perspective is primarily based on topological properties though it also employs semitensor-product and...
Oxford: Elsevier, 2006. — 460 p. — ISBN 0444521976, 9780080462462. This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important...
Singapore: Springer, 2017. — 278 p. This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research...
MDPI AG, 2025. — 374 p. Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in the fields of physics and mathematics, among others, as highly correlated nonlinear phenomena, evolving over a large range of time and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed,...
Springer, 2011. — 538 p. — ISBN 978-94-007-0731-3.
Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics....
Springer, 2018. —239 p. — (Probability Theory and Stochastic Modelling 90). — ISBN: 978-1-4939-8833-4. This book undertakes a detailed construction of Dynamic Markov Bridges using a combination of theory and real-world applications to drive home important concepts and methodologies. In Part I, theory is developed using tools from stochastic filtering, partial differential...
6th Edition. — Springer, 2003. — 360 pages. — ISBN: 3540047581.
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start...
Учебное пособие. — Самара: Изд-во Самар. гос. аэрокосм. ун-та, 2010. — 93 с. Пособие посвящено описанию методов исследования нелинейных колебаний механических систем. В пособии представлены как классические результаты теории нелинейных колебаний, так и асимптотические методы нелинейной механики. Рассмотрены примеры применения методов теории нелинейных колебаний к исследованию...
Алматы: Қазақ университеті, 2014. — 158 с. Монография посвящена проблемам управляемости и оптимального быстродействия процессов, описываемых обыкновенными дифференциальными уравнениями и параболическим уравнением. Созданы методы построения программных и позиционных управлений при наличии краевых условий, а также фазовых и интегральных ограничений с учетом ограничений на...
Учебное пособие. — Новосибирск: Новосибирский государственный технический университет (НГТУ), 2023. — 70 с. Настоящее учебное пособие содержит материал по теории динамических систем и методам их качественного исследования. Приведены основы бифуркационного анализа динамических систем. Цель пособия – показать эффективность методов и приемов качественного исследования динамических...
Учебное пособие. — Самара: Самарский университет, 2022. — 88 с. В данном пособии рассмотрены основные методы получения приближенных аналитических решений дифференциальных уравнений и их систем, содержащих малый параметр. Описаны методы малого параметра и методы разложения движений на быстрые и медленные. Данные методы применяются при исследовании движения механических систем и...
М.: Изд-во МГУ, 2000. — 173 с. Книга написана на основе лекций, читаемых авторами в течение ряда лет для студентов старших курсов физического факультета МГУ. Курс лекций ставит своей целью ознакомить студентов с относительно новым разделом математической физики — теорией особенностей отображений множеств, называемой также иногда теорией катастроф, и ее приложениями в физике....
Учебное пособие. — Ярославль: Ярославский государственный университет им. П. Г. Демидова (ЯрГУ), 2018. — 64 с. Учебное пособие посвящено проблеме отыскания числовых характеристик динамических систем с хаотическим поведением. Оно включает в себя краткое изложение теоретических основ применяемых методов, которое проиллюстрировано подробным разбором ряда задач, и материалы для...
Монография. — М.: Наука, 1967. — 488 с. Предлагаемая монография непосредственно примыкает к вышедшей в 1966 г. книге тех же авторов «Качественная теория динамических систем второго порядка» (КТ) и может рассматриваться как ее продолжение и как второй том задуманной (еще в 40-х годах) А. А. Андроновым монографии по динамическим системам и их приложениям. Однако необходимо...
Монография. — М.: Наука, 1967. — 488 с. Предлагаемая монография непосредственно примыкает к вышедшей в 1966 г. книге тех же авторов «Качественная теория динамических систем второго порядка» (КТ) и может рассматриваться как ее продолжение и как второй том задуманной (еще в 40-х годах) А. А. Андроновым монографии по динамическим системам и их приложениям. Однако необходимо...
Саратов, Берлин, Сент-Луис: Издательство не указано, 2004. — 535 с. Настоящая книга представляет собой фундаментальный труд по основам нелинейной динамики хаотических и стохастических систем. Книга включает исчерпывающее введение в теорию динамических и стохастических систем и детальный анализ современных результатов, в основном полученных авторами. Каждая из глав книги...
Саратов, Берлин, Сент-Луис: Издательство не указано, 2011. — 535 с. Настоящая книга представляет собой фундаментальный труд по основам нелинейной динамики хаотических и стохастических систем. Книга включает исчерпывающее введение в теорию динамических и стохастических систем и детальный анализ современных результатов, в основном полученных авторами. Каждая из глав книги построена...
Институт компьютерных исследований. Год издания: 2002. Количество страниц: 143. В книге представлены 10 лекций по теоретическим основам нелинейной динамики систем с конечным числом степеней свободы (в третье издание лекций, по сравнению с первым, добавлены 3 лекции). Для обсуждения в книге выбраны ряд ключевых проблем, которые относятся к фундаментальным основам нелинейной...
М.: Наука, 1990. — 312 с. Книга подробно рассматривает предмет компьютерного моделирования. Подходит для научных работников, инженеров-исследователей, аспирантов и студентов. Вот некоторые из глав книги: Динамическая система и ее мат. модель Классификация динамических систем Дифференциальные уравнения Колебательные системы. Свойства Фазовые портреты типовых колебательных систем....
М.: Наука, 1990. — 312 с. Методами численного и физического экспериментов исследуются общие закономерности развития и свойства хаотических колебаний на примере радиофизических систем. Анализируются типичные бифуркации регулярных к странных аттракторов, вызываемые изменением параметров и воздействием флуктуаций. Обосновывается методика экспериментальных исследований динамического...
Москва; Ижевск: Научно-издательский центр «Регулярная и хаотическая динамика», 2008. - 144 с. Книга посвящена систематическому изложению результатов теоретического, численного и экпериментального анализа эффектов синхронизации периодических, квазипериодических, хаотических и стохастичеческих колебаний. Подробно излагается классическая теория синхронизации и обсуждаются пределы...
Учебное пособие для студентов высших учебных заведений обучающихся по специальностям «Радиофизика и электроника», «Физика». — Саратов: СГУ, 2010. — 322 с. В лекционном курсе по фундаментальным аспектам нелинейной динамики детерминированных и стохастических систем излагаются основы теории динамических систем, теории устойчивости и бифуркаций, теории фракталов и размерности;...
Москва, Ижевск: НИЦ "Регулярная и хаотическая динамика". 2011. — 516 c. — ISBN: 978-5-93972-920-8
Качество: Хороший скан
В лекционном курсе по фундаментальным аспектам нелинейной динамики детерминированных и стохастических систем излагаются основы теории динамических систем, теории устойчивости и бифуркаций, теории фракталов и размерности; анализируются основные нелинейные...
М.: ВИНИТИ, 1986. — 284 с. Итоги науки и техники. Серия "Современные проблемы математики. Фундаментальные направления". Том 5, Научный редактор член-корреспондент АН СССР Р. В. Гамкрелидзе. Серия издается с 1985 г. Обзор посвящен теории бифуркаций в динамических системах. Наряду с известными, обзор включает ряд новых результа-результатов; некоторые из них известны авторам из...
3-е изд., доп. — М.: Наука, 1990. — 128 с. Математическое описание катастроф - скачкообразных изменений, возникающих в виде внезапного ответа на плавное изменение внешних условий, дается теориями особенностей и бифуркаций. Их применения к конкретным задачам науки вызвали много споров. В книге рассказывается о том, что же такое теория катастроф и почему она вызывает такие споры....
3-е изд., доп. — М.: Наука, 1990. — 128 с. Математическое описание катастроф - скачкообразных изменений, возникающих в виде внезапного ответа на плавное изменение внешних условий, дается теориями особенностей и бифуркаций. Их применения к конкретным задачам науки вызвали много споров. В книге рассказывается о том, что же такое теория катастроф и почему она вызывает такие споры....
2-е изд., доп. — М.: Изд-во МГУ, 1983. — 80 с. — (Новые идеи в естествознании). Катастрофами называются скачкообразные изменения, возникающие в виде внезапного ответа системы на плавное изменение внешних условий. Источниками теории катастроф являются теория особенностей гладких отображений и теория бифуркаций динамических систем. Их применения к конкретным задачам в разных...
3-е изд., доп. — М.: Наука, 1990. — 128 с. Математическое описание катастроф - скачкообразных изменений, возникающих в виде внезапного ответа на плавное изменение внешних условий, дается теориями особенностей и бифуркаций. Их применения к конкретным задачам науки вызвали много споров. В книге рассказывается о том, что же такое теория катастроф и почему она вызывает такие споры....
3-е изд., доп. — М.: Наука, 1990. — 128 с. Математическое описание катастроф - скачкообразных изменений, возникающих в виде внезапного ответа на плавное изменение внешних условий, дается теориями особенностей и бифуркаций. Их применения к конкретным задачам науки вызвали много споров. В книге рассказывается о том, что же такое теория катастроф и почему она вызывает такие споры....
Итоги науки и техники. Серия "Современные проблемы математики. Фундаментальные направления". Том 6, научный редактор член-корреспондент АН СССР Р. В. Гамкрелидзе, М. : 1988. - 275 с. Этот научный труд знакомит читателя с основными понятиями теории особенностей дифференцируемых отображений, приводит начальный отрезок классификации гладких функций и излагает технику приведения...
Итоги науки и техники. — Научный редактор член-корреспондент АН СССР Р. В. Гамкрелидзе. — М.: ВИНИТИ, 1989. — 255 с. — (Современные проблемы математики. Фундаментальные направления". Том 39). Хотя основной задачей авторов было единое изложение уже сформировавшейся теории, читатель встретит в томе и совсем недавние результаты, по-видимому, не известные еще даже специалистам....
Новосибирск: СО РАН, 2016. — 292 c.
В монографии рассматриваются вопросы численного статистического моделирования решений систем стохастических дифференциальных уравнений (СДУ ) на многопроцессорных суперкомпьютерах. Проводится численный анализ решений систем СДУ , описывающих линейные и нелинейные стохастические колебания. Особое внимание уделяется анализу поведения решений...
Электронное учебное пособие. – Самара: Изд-во Самар. гос. аэрокосм. ун-та, 2010. – 92 с. В пособии изложен ряд базовых идей и методов, применяемых для исследования нелинейных механических систем. Излагаются классические результаты теории динамических систем: структурная устойчивости, аналитические методы локальной теории в окрестности особой точки, нормальные формы, теория...
Учебное пособие. — Самара: Изд-во Самар. гос. аэрокосм. ун-та, 2010. — 53 с. Целью данного пособия является практическое знакомство студентов с методами нелинейной динамики. Практикум состоит из пяти частей, в каждой из которых приводится необходимый теоретический материал, пример и тридцать вариантов практических заданий для самостоятельного выполнения. Для выполнения...
Горький, ИПФ АН СССР, 1989. — 256 с. Рассматривается нелинейная динамика дискретных неравновесных сред - сетей автоматической синхронизации цепочечного и решеточного типа. Изучаются вопросы установления режима синхронизации, возможные пути потери синхронизации, в част ности связанные с возникновением динамического хаоса, а также вопросы образования пространственных структур в...
Горький: ИПФ АН СССР, 1989. — 256 с. Рассматривается нелинейная динамика дискретных неравновесных сред — сетей автоматической синхронизации цепочечного и решеточного типа. Изучаются вопросы установления режима синхронизации, возможные пути потери синхронизации, в частности связанные с возникновением динамического хаоса, а также вопросы образования пространственных структур в...
М.: Наука, 2001. — 352 с. В книге рассматриваются теоретические и практические проблемы управления структурами, существенноотличащиеся от проблем управления состояниями. Вводятся основные понятия теории управления. Выясняется связь понятия "управление" с понятиями современной теоретической физики. Излагается ряд новых результатов по исследованию структур управления.
М.: Наука и техника, 1979. — 120 с. Исследуются общие динамические системы. С помощью метода сечений найдены необходимые и достаточные условия выпрямляемости, гармонизуемости динамических систем, необходимое и достаточное условие существования секущей поверхности. Рассматривается вопрос о существовании решений уравнений в частных производных. Полученные результаты связываются с...
Учеб. пособие. — Екатеринбург: Изд-во Урал. ун-та, 2017. — 84 с. — ISBN: 978-5-7996-2046-2. Учебное пособие является вводным курсом в методы моделирования и анализа разнообразных явлений нелинейной динамики, способствует развитию понимания внутренних механизмов сложных динамических процессов как детерминированных, так и стохастических систем, выработке навыков их компьютерного...
Учебное пособие. — Саратов: Изд-во ГосУНЦ Колледж, 2001. — 44 с. Рассматриваются подходы к построению модельных дифференциальных уравнений по временным рядам – последовательностям значений наблюдаемой величины, измеренных в дискретные моменты времени. Наиболее сложной, творческой, неподдающейся алгоритмизации частью такого моделирования яв-ляется выбор структуры уравнений. Если...
Саратов: Колледж, 2005. — 320 с. В книге излагаются общие вопросы моделирования и проблемы создания математических моделей эволюции (движений, процессов) по временным рядам - дискретным последовательностям экспериментально измеренных значений наблюдаемых величин. Основное внимание уделяется динамическому (детерминистическому) подходу к моделированию с присущей ему претензией на...
Саратов: Колледж, 2005. В книге излагаются общие вопросы моделирования и проблемы создания математических моделей эволюции (движений, процессов) по временным рядам дискретным последовательностям экспериментально измеренных значений наблюдаемых величин. Основное внимание уделяется динамическому (детерминистическому) подходу к моделированию с присущей ему претензией на точность...
Саратов: Колледж, 2005. — 320 с. — ISBN: 5944090456. В книге излагаются общие вопросы моделирования и проблемы создания математических моделей эволюции (движений, процессов) по временным рядам - дискретным последовательностям экспериментально измеренных значений наблюдаемых величин. Основное внимание уделяется динамическому (детерминистическому) подходу к моделированию с...
Учебно-методическое пособие. — Саратов: Колледж, 2000. — 39 с. Рассматриваются подходы к построению динамических моделей с дискретным временем (точечных отображений) по скалярным временным рядам, не имеющим видимой закономерности. Описаны методы глобальной и локальной реконструкции отображений. Предлагается, пользуясь готовыми программами, получить хаотические временные реализации...
Учебно-методическое пособие. — Саратов: Колледж, 2000. — 46 с. Рассматриваются подходы к построению динамических моделей с непрерывным временем по временным рядам. Демонстрируются методы глобальной реконструкции обыкновенных дифференциальных уравнений по векторным и скалярным рядам. Описываются приемы уменьшения влияния шумов. В практической части предлагается, пользуясь готовыми...
Саратов: Колледж, 2000. — 23 с. Рассматриваются подходы к использованию дискретных последовательностей экспериментальных данных (временных рядов) для конструирования статистических моделей, предназначенных для прогноза поведения объекта. Представлены: экстраполяция временной зависимости, а также линейные модели авторегрессии и проинтегрированного скользящего среднего....
Ижевск: Удмуртский университет, 1999. — 408 с. Классическая монография одного из значительных математиков этого века. После выхода этой книги динамические системы стали отдельной интенсивно развивающейся областью математики. Предназначена для студентов и аспирантов, физиков и математиков, полезна для научных сотрудников и преподавателей. Предисловие Предисловие редакторов...
Монография. — Ижевск: Удмуртский университет, 1999. — 408 с. Классическая монография одного из значительных математиков этого века. После выхода этой книги динамические системы стали отдельной интенсивно развивающейся областью математики. Предназначена для студентов и аспирантов, физиков и математиков, полезна для научных сотрудников и преподавателей.
Перевод с английского 3.С. Воронина и Ю.А. Янайта. — Под редакцией Р.В. Хохлова. — М.: Мир, 1969. — 400 с. Теория колебаний — это раздел физики, имеющий исключительно широкую область применений. С колебательными процессами мы встречаемся в электронике, электротехнике и радиотехнике, системах связи, физической акустике, оптике, газовой динамике, инженерной механике,...
Перевод с английского 3.С. Воронина и Ю.А. Янайта. — Под редакцией Р.В. Хохлова. — М.: Мир, 1969. — 400 с. Теория колебаний — это раздел физики, имеющий исключительно широкую область применений. С колебательными процессами мы встречаемся в электронике, электротехнике и радиотехнике, системах связи, физической акустике, оптике, газовой динамике, инженерной механике,...
М.: Вузовская книга, 2008. — 428 с. В книге излагаются новые результаты, методы и приемы исследований фазовых портретов динамических систем на плоскости (в основном с непрерывным временем, но в ряде случаев и с дискретным временем). Приводится их полное обоснование, доказательство вспомогательных лемм и теорем, а также примеры, показывающие их эффективность. Ответы в примерах...
Киев: Наукова думка, 1969. — 253 с. Монография посвящена изложению ряда новых результатов нелинейной механики, полученных с помощью модернизированного Η. Н. Боголюбовым метода последовательных замен переменных, обеспечивающего ускоренную сходимость. Метод последовательных замен, предложенный еще в 1934 г. Η. М. Крыловым и Η. Н. Боголюбовым, явился эффективным аппаратом для решения...
Киев: Наукова думка, 1969. — 253 с.
Монография посвящена изложению ряда новых результатов нелинейной механики, полученных с помощью модернизированного Η. Н. Боголюбовым метода последовательных замен переменных, обеспечивающего ускоренную сходимость.
Метод последовательных замен, предложенный еще в 1934 г. Η. М. Крыловым и Η. Н. Боголюбовым, явился эффективным аппаратом для...
Учебно-методическое пособие. — Нижний Новгород: Нижегородский госуниверситет, 2017. — 73 с. Одной из самых важных бифуркаций для потоков и отображений в нелинейной динамике является бифуркация Андронова-Хопфа, часто встречающаяся в математических моделях реальных систем. Цель данного пособия – дать представление о современном состоянии теории нелинейных динамических систем в...
Екатеринбург: УрО РАН, 2010. — 408 с. (Научно-образовательная серия «Физика конденсированных сред»; 3). — ISBN: 978-5-7691-2145-6. В книге рассмотрены основные принципы теоретической механики, методы аналитической механики и дан краткий очерк их развития. Большое внимание уделено изложению наиболее содержательных и ценных для теории и приложений разделов нелинейной динамики:...
459 с. Книга посвящена одному из актуальных направлений в современной теоретической физике - пуассоновым структурам и их приложениям к различным проблемам гамильтоновой механике. Эти задачи возникают в динамике твердого тела, небесной механике, теории вихрей, космологических моделях. Как правило, уравнения движения таких систем можно записать в удобной полиномиальной...
М.: Мир, 1979. — 248 с. — (Новое в зарубежной науке. Математика. Выпуск 13).
Книга представляет собой сборник переводов недавних работ известного американского математика. В них исследуются топологические и метрические свойства классических динамических систем, удовлетворяющих условию гиперболичности.
Пер. с англ. под ред. А. В. Савина — М.: Физматлит, 2008. — 536 с. В книге известных специалистов по нелинейной динамике и теории солитонов О. М. Брауна и Ю. С. Кившаря систематически изложены, с наиболее общей точки зрения, концепции и методы низкоразмерной нелинейной физики, базирующиеся на модели ФК и ее обобщениях. Представлен панорамный взгляд на общие свойства и...
Волгоград: Платон, 1997. — 208 с. — (Современная математика. Вводные курсы). — ISBN 5-80100-174-3 Данное издание является факсимильным. Из аннотации к изданию 1977 года (М.: Мир): Первое в мировой литературе учебное пособие по так называемой теории катастроф (теории бифуркаций критических точек функций). Проблемы, которые ставятся и решаются в этой теории, постоянно возникают...
Волгоград: Платон, 1997. — 208 с. — (Современная математика. Вводные курсы). — ISBN: 5-80100-174-3 Данное издание является факсимильным. Из аннотации к изданию 1977 года (М.: Мир): Первое в мировой литературе учебное пособие по так называемой теории катастроф (теории бифуркаций критических точек функций). Проблемы, которые ставятся и решаются в этой теории, постоянно возникают...
Москва-Ижевск: Институт компьютерных исследований, 2003. - 336 с.
Книга известных математиков, преподающих в университетах Голландии и Бельгии, охватывает основные разделы нелинейной динамики и теории детерминированного хаоса. Предназначена для студентов и аспирантов университетов, специалистов по динамическим системам.
Москва-Ижевск: Институт компьютерных исследований, 2003. - 336 с.
Книга известных математиков, преподающих в университетах Голландии и Бельгии, охватывает основные разделы нелинейной динамики и теории детерминированного хаоса. Предназначена для студентов и аспирантов университетов, специалистов по динамическим системам.
Сборник лекций. — Москва: Научный совет по акустике АН СССР, 1970. — 450 с. С 15 июля по 5 августа 1968 года в городе Улан-Удэ проводились занятия 2-й Всесоюзной летней школы по дифракции и распространению волн, организованной Научным Советом по акустике АН СССР и Министерством радиопромышленности СССР при содействии Института естественных наук Бурятского филиала Сибирского...
2-е изд., перераб. — М.: Наука, 1987. — 382 с.: ил.
Изложены основные вопросы теории нелинейных колебаний, начиная с исходных, прочно вошедших в науку, и кончая вопросами, вводящими читателя в ее современное состояние. Рассмотрены как точные, так и приближенные методы научной школы Мандельштама — Андронова. Вместе с тем в книге нашли определенное отражение идеи и методы,...
2-е изд., перераб. — М.: Наука, 1987. — 382 с.: ил.
Изложены основные вопросы теории нелинейных колебании, начиная с исходных, прочно вошедших в науку, и кончая вопросами, вводящими читателя в ее современное состояние.
Рассмотрены как точные, так и приближенные методы теории нелинейных колебаний. Особое место занимают: методы научной школы Мандельштама — Андронова. Вместе с...
М.: Наука, 1985. — 136 с. — (Теоретические основы технической кибернетики). Излагается новый метод исследования систем управления отличающийся большой наглядностью. На основе выведенных уравнений границ интегральных воронок, описывающих управляемые динамические системы, вводится и изучается понятие фазового портрета этой системы, который дает полное качественное представление...
М.: Наука, 1985. — 136 с.
Излагается новый метод исследования систем управления, отличающийся большой наглядностью. На основе выведенных уравнений границ интегральных воронок, описывающих управляемые динамические системы, вводится и изучается понятие фазового портрета этой системы, который дает полное качественное представление свойств системы и позволяет конструктивно решать...
М.: Наука, 1984. — 256 с. В книге излагается систематический подход с позиций теории управления к проблеме целенаправленного воздействия на микропроцессы, описываемые квантовомеханическими закономерностями. Даются точные постановки задач управления, в том числе оптимального управления, оптимизации и управляемости, сформулированные в терминах чистых и смешанных состояний квантовых...
М.: МЦНМО, 2005. — 416 с. В книге изложены некоторые методы и результаты теории бифуркаций векторных полей на плоскости. Излагаются элементы теории центральных многообразий и нормальных форм. Подробно рассматриваются все известные бифуркации коразмерности два векторных полей на плоскости, а также некоторые бифуркации большей коразмерности. Для студентов, аспирантов и научных...
М., Наука, 1987 - 240 с. В монографии приводится обзор основных экспериментальных фактов автоволновых процессов из физики, химии и биологии. Предлагается классификация этих данных. Строятся основные типы математических моделей и приводится их качественный анализ. Рассматривается роль флуктуаций. Внимание сосредотачивается на проблемах образования структур в системах, далеких от...
Монография. — М.: Наука, 1987. — 240 с. В монографии приводится обзор основных экспериментальных фактов автоволновых процессов из физики, химии и биологии. Предлагается классификация этих данных. Строятся основные типы математических моделей и приводится их качественный анализ. Рассматривается роль флуктуаций. Внимание сосредотачивается на проблемах образования структур в...
М.; Ижевск: НИЦ РХД; ИКИ. — 164 с. В пособии излагаются элементы теории хаотического поведения (детерминированного хаоса) простейших дискретных и непрерывных динамических систем и обсуждаются основные понятия фрактальной геометрии.
М.: Наука, 1979. — 424 с. Книга посвящена изучению случайных процессов, определяемых дифференциальными уравнениями, правые части которых претерпевают случайные возмущения. Подобные задачи часто встречаются как в практических, так и в теоретических исследованиях. При исследовании таких процессов важную роль играют асимптотические методы, которые применимы, если возмущения в том...
Монография. — Саров: РФЯЦ-ВНИИЭФ, 2016. — 267 с. — ISBN: 978-5-9515-0324-4. Монография посвящена динамике систем с цилиндрическим фазовым пространством. Данный класс моделей охватывает механические, квантово-механические, радиотехнические и многие другие системы из различных областей естествознания и технических приложений. Рассматриваются автономные и неавтономные системы с...
Саров: Российский федеральный ядерный центр – ВНИИЭФ, 2018. — 338 с. Исследуются современные проблемы нелинейной динамики, возникающие в контексте динамического хаоса. Особое внимание уделяется синхронизации систем с хаотической динамикой – хаотической синхронизации: ее истории, свойствам и перспективам приложений. Рассматриваются: задачи устойчивости хаотической синхронизации...
Баку: ELM, 2011. — 240 с. Книга посвящена визуальному представлению и анализу инвариантных множеств при реализации задач управления хаотическими системами. В качестве интеллектуальной поддержки, принимаемых субъектом решений, рассматривается синергетический подход к синтезу систем управления нелинейными процессами, идеологической основой которого являются теория...
Учебное пособие. — Самара: Самарский университет, 2014. — 88 с. — ISBN 9785864656396. В учебном пособии излагаются основные положения общей теории теории уравнений и систем с дискретным временем. Базовые понятия иллюстрируются примерами. Наряду с широко известными результатами приводятся оригинальные результаты авторов. Особое внимание уделяется анализу дискретных нелинейных...
Итоги науки и техники. — М.: ВИНИТИ, 1987. — 322 с. Неголономные динамические системы. Геометрия распределений и вариационные задачи. (А.М. Вершик, В.Я. Гершкович) Интегрируемые системы. II. Интегрируемые системы и конечномерные алгебры Ли (М.А. Ольшанецкий, А.М. Переломов) Теоретико-групповые методы в теории интегрируемых систем (А.Г. Рейман, М.А. Семенов-Тян-Шанский)...
М.: Наука, 1976. — 368 с.
В книге рассматриваются вопросы теории нелинейных колебаний, метода точечных преобразований и теории автоматического управления.
Излагаются основы теории динамических систем, метода точечных преобразований и теории бифуркаций. Изучаются различные классы автономных и неавтономных систем 2-го, 3-го и 4-го порядков, встречающихся в задачах...
Пер, с англ. — М,: Мир, 1984. — 350 с, ил.
Монография известного американского ученого посвящена теории катастроф и ее приложениям в различных областях науки и техники. В русском переводе монография выходит в двух книгах. В книге 1 рассматриваются основные понятия теории катастроф и применение ее методов в физике, механике, математике, термодинамике и аэродинамике.
Для...
Пер. с англ. — М.: Мир, 1984. — 285 с, ил.
Монография известного американского ученого посвящена теории катастроф и ее приложениям в различных областях науки и техники. В русском переводе монография выходит в двух книгах. В книге 2 рассматриваются математические основы теории катастроф и применение ее методов в квантовой механике, климатологии и других областях, а также вопросы,...
Перевод книги выполнен И. И. Чижиковым, С. П. Чеботаревым, Д. А. Казениным, О. П. Бердышевой. — М.: 1981. — 344 с. Теория катастроф как исследовательская программа. Локальный характер потенциальных функций. Замена переменных. Канонические формы. Возмущения. "Принцип лома". Геометрия складки и сборки. Организация катастроф. Принцип максимального продления и принцип Максвелла. Флаги...
М.: Мир, 1984. — 285 с. Монография известного американского ученого посвящена теории катастроф и ее приложениям в различных областях науки и техники. В русском переводе монография выходит в двух книгах. В книге 2 рассматриваются математические основы теории катастроф и применение ее методов в квантовой механике, климатологии и других областях, а также вопросы, связанные с...
Монография. — М.: Янус-К, 1999. — 331 c. Основной математический объект, изучаемый в монографии, — это регулярные по малому параметру многочастотные системы обыкновенных дифференциальных уравнений с медленными и быстрыми фазовыми переменными, в которых возможны резонансные соотношения между основными частотами. Дана классификация резонансных систем, в основу которой положена идея...
М.: Янус-К, 1999. — 312 с. Основной математический объект, изучаемый в монографии, — это регулярные по малому параметру многочастотные системы обыкновенных дифференциальных уравнений с медленными и быстрыми фазовыми переменными, в которых возможны резонансные соотношения между основными частотами. Дана классификация резонансных систем, в основу которой положена идея о застревании...
Москва: Наука, 1979. — 431 с. Книга посвящена теории асимптотических и итерационных методов, применяющихся при решении задач резонансного типа. В первой части рассматриваются асимптотические методы решения нелинейных уравнений, основанные на различных схемах усреднения. Много места уделено приложениям: задачам теории колебаний и небесной механики, гидродинамики, теории упругости....
Статья. Москва: Российский университет дружбы народов, 2010. — 46 с. В статье критически анализируется подход к согласованию термодинамической необратимости с обратимостью механики, основанный на понятии «тонкой» энтропии. Показывается обоснованность интерпретации необратимости, разработанной Смолуховским.
М.: КомКнига, 2006. — 208 с. (Синергетика: от прошлого к будущему.) Издание 2-е, исправленное. В основу книги легли лекции, которые читались на химическом факультете МГУ им. М.В. Ломоносова, в СГУ им. Н.Г. Чернышевского, а также в МИФИ и университетах Западной Европы. В пособии подробно изложены дискретные отображения и теория непрерывных систем, хаотическое поведение,...
Издание 2-е, исправленное — М.: КомКнига, 2006. — 208 с. (Синергетика: от прошлого к будущему.) В основу книги легли лекции, которые читались на химическом факультете МГУ им. М.В. Ломоносова, в СГУ им. Н.Г. Чернышевского, а также в МИФИ и университетах Западной Европы. В пособии подробно изложены дискретные отображения и теория непрерывных систем, хаотическое поведение,...
Учебное пособие. — Самара: Самарский государственный аэрокосмический университет, 2008. — 100 с. — ISBN: 978-5-7883-0584-4. Рассматриваются вопросы математического моделирования и качественного анализа динамических систем, возникающих в задачах теоретической механики и нелинейной динамики. Приводятся основные понятия теории динамических систем и описываются возможные...
Учебное пособие. — Самара: Самарский государственный аэрокосмический университет, 2008. — 100 с. — ISBN: 978-5-7883-0584-4. Рассматриваются вопросы математического моделирования и качественного анализа динамических систем, возникающих в задачах теоретической механики и нелинейной динамики. Приводятся основные понятия теории динамических систем и описываются возможные...
Ижевск: Регулярная и хаотическая динамика, 2010. - 345с.
Теорема Понселе является одним из красивейших и важнейших результатов проективной геометрии. В данной книге впервые в мировой литературе систематическим образом изложены теоремы типа Понселе, а также их естественные более многомерные обобщения и приложения в области механики и геометрии. Основная цель этой книги...
Учеб. метод. пособие. — Н. Новгород: Изд-во ННГУ, 2007. — 89 с.
Книга посвящена описанию авторской программы WlInSet и ее использованию для анализа большого набора задач из физики, механики, биологии, химии, экономики и др. путем построения инвариантных множеств соответствующих динамических систем (фазовых кривых, резонансных структур, странных аттракторов, фракталов, паттернов...
СПб.: Наука, 2005. — 314 с.
В книге представлены теоретические основы и методы робастного и адаптивного управления нелинейными колебательными системами, характеризуемые высокой размерностью и существенной нелинейностью математических моделей. Особенностью изложения является использование результатов теории устойчивости динамических систем от входа к выходу для анализа и синтеза...
Монография. — Изд-е 2-е. — Москва: МФТИ, 1996. — 344 с. — ISBN 5-89269-002-4. Представляемая монография является результатом многолетних исследований автора и его учеников в области динамической теории неустойчивых нелинейных систем. Она является вторым изданием книги [1]. Стимулом для написания первого издания «Динамики неустойчивостей» послужили пять лекций, прочитанных...
Учебное пособие. — Новосибирск: НГУ, 2014. — 71 с. Курс лекций по избранным вопросам нелинейной и хаотической динамики для студентов Новосибирского государственного университета физического факультета. Список литературы. Классическая динамика нелинейных систем. Введение в основы гамильтоновой динамики. Уравнения Гамильтона. Скобки Пуассона. Канонические преобразования....
Петрозаводск: КарНЦ РАН, 2013. — 505 с., ил. — ISBN: 978-5-9274-0581-7. В книге изложены методы решения задач прогнозирования фазового состояния нелинейных динамических систем, оценивания функционалов на решениях систем с запаздыванием и параметрической идентификации распределенных моделей водородопроницаемости конструкционных материалов с нелинейными динамическими граничными...
Петрозаводск: КарНЦ РАН, 2013. — 505 с.: ил. — ISBN: 978-5-9274-0581-7. В книге изложены методы решения задач прогнозирования фазового состояния нелинейных динамических систем, оценивания функционалов на решениях систем с запаздыванием и параметрической идентификации распределенных моделей водородопроницаемости конструкционных материалов с нелинейными динамическими граничными...
Монография. — М.: Наука. Главная редакция физико-математической литературы, 1970. — 143 с. —(Современные проблемы физики) Предлагаемая монография посвящена анализу условий, при которых динамическую систему можно описывать статистическими методами без априорных предположений о наличии в системе случайных параметров. Этот вопрос тесно связан с проблемой обоснования статистической...
М.: Наука, 1984. – 272 с.
Книга посвящена систематическому описанию явления стохастичности, или хаоса, которое возникает при определенных условиях в нелинейных динамических системах и появление которого не обусловлено действием каких-либо случайных сил на систему. Книга содержит изложение вопросов теории хаоса общего характера, а также приложения из различных областей физики...
М.: МЦНМО, 2005. — 16 с. Рассматриваются различные типы отображений, порождающие как странные, так и классические аттракторы. От читателя не требуется никаких начальных знаний из теории дифференциальных уравнений. Брошюра адресована старшим школьникам и студентам младших курсов. Эволюционные процессы. Аттракторы. Странные аттракторы: Канторово совершенное множество; соленоид...
М.: МЦНМО, 2011. –– 128 с. — ISBN: 978-5-94057-818-5. Теория динамических систем делится на две части: многомерные системы (царство хаоса) и маломерные (царство порядка). К первой, более обширной области относятся эпиморфизмы в любой размерности, диффеоморфизмы в размерности 2 и потоки в размерности три и выше. Ко второй относятся диффеоморфизмы окружности и векторные поля на...
Учебно-методическое пособие для студентов 4 курса факультета нелинейных процессов. — Саратов: СГУ, 2012. — 78 с. Пособие предназначено для использования при проведении занятий по курсу «Физика фракталов» у студентов 4 курса факультета нелинейных процессов. Может быть полезно как студентам, изучающим теорию фракталов, теорию динамических систем, теорию хаоса, нелинейную динамику и...
Учебное пособие. — Нижний Новгород: Нижегородский госуниверситет, 2011. — 84 с. Цель пособия — ознакомить читателя с современными методами анализа динамики консервативных решеточных систем с непрерывным временем на примере эффектов локализации энергии в решеточных системах (дискретные бризеры, модуляционная неустойчивость). Внимание уделяется особенностям динамики решеточных...
М.; Л.: Госэнергоиздат, 1962. — 457 с. Ориентированное на инженеров (преимущественно в области электро- и радиотехники и автоматического регулирования) изложение способов решения нелинейных дифференциальных уравнений (включая уравнения с запаздыванием). Рассмотрены аналитические и численные методы, дополнительное внимание уделено колебательным системам и вопросам устойчивости.
Навчальний посібник. — Луцьк: Вежа-Друк, 2020. — 348 с. Навчальний посібник висвітлює сучасні напрямки теорії диференціальних рівнянь та динамічних систем. Книга адресована викладачам, аспірантам, студентам вузів, які здобувають фах за освітніми програмами Математика, Компʼютерна математика, Прикладна математика, Середня освіта (Математика) та спеціалізуються в області теорії...
М.: МГИУ, 2008. – 160 с. Рассмотрены вопросы структурной идентификации динамических систем на основе анализа наблюдаемых информационных портретов в условиях неопределенности. Предложены методы оценки состояния равновесия динамической системы. Описаны процедуры нахождения собственных чисел динамической системы. На основе информационного синтеза разработан метод оценки нелинейной...
М.: Наука, 1973. — 175 с. Книга посвящена изложению с единой точки зрения широкого круга вопросов теории нелинейных волн в средах с дисперсией и диссипацией. Эта сравнительно молодая бурно развивающаяся область нелинейной динамики вызывает в настоящее время значительный интерес у специалистов, работающих в самых различных областях. Основное внимание уделяется нестационарным...
М.: Факториал, 1999. — 768 с. В книге содержится чрезвычайно полное и подробное изложение теории динамических систем как ключевой математической дисциплины, тесно связанной с большинством областей математики. Развивая теорию авторы объясняют фундаментальные понятия теории и рассматривают их на многочисленных примерах. Книга предназначена студентам, аспирантам и научным сотрудникам...
М.: Факториал, 1999. — 768 с. В книге содержится чрезвычайно полное и подробное изложение теории динамических систем как ключевой математической дисциплины, тесно связанной с большинством областей математики. Развивая теорию авторы объясняют фундаментальные понятия теории и рассматривают их на многочисленных примерах. Книга предназначена студентам, аспирантам и научным...
Перевод с английского под редакцией А.С.Городецкого. — М.: МЦНМО, 2005. — 464 с. — ISBN: 5-94057-063-1. В книге изложены некоторые методы и результаты теории бифуркаций векторных полей на плоскости. Излагаются элементы теории центральных многообразий и нормальных форм. Подробно рассматриваются все известные бифуркации коразмерности два векторных полей на плоскости, а также...
Рига: Зинатне, 1990. — 189 с. Предложено несколько простых эвристических методов получения явных аналитических решений (локализованных и периодических) обыкновенных автономных нелинейных дифференциальных уравнений, у которых дифференциальная функция является полиномом по динамической переменной и ее производным. Рассмотренные уравнения отвечают односолитонным (в случае...
Изд. 2-е. — М.: Либроком, 2013. — 288 с. — (Синергетика: от прошлого к будущему. №43). В настоящей книге рассматриваются модели нейронной среды, описываемой системой уравнений с запаздыванием. Каждый элемент среды (нейрон) является автогенератором, который в автономном режиме генерирует кратковременные импульсы (спайки). Обсуждаются модели синаптического взаимодействия...
2001. — 98 с. Это учебное пособие написано по курсу лекций, прочитанному во время весеннего семестра 1999 года студентам Уфимского Государственного Авиационного Технического Университета, специализирующимся по прикладной математике. Линейные системы. Уравнение Штурма-Лиувилля с периодическим коэффициентом. Математический маятник. Эллиптические функции.
М.: Бином. Лаборатория знаний, 2009. — 648 с. — (Математическое моделирование). — ISBN: 978-5-94774-899-4. Монография посвящена разработке континуальных моделей турбулизованных природных сред — моделей, лежащих в основе постановок и численных расчетов задач, связанных с образованием, структурой и эволюцией различных астро- и геофизических объектов. Стохастические модельные...
Учебное пособие. — Сибирский государственный индустриальный университет. — Новокузнецк, 2006. — 106 с.
Учебное пособие содержит материалы, предусмотренные программой учебной дисциплины «Основы нелинейной динамики». Учебное пособие посвящено исследование простейших нелинейных моделей, представленных в форме дискретных отображений, одномерных и многомерных. Исследование таких...
М.; Ижевск: Регулярная и хаотическая динамика, Институт компьютерных исследований, 2007. — 576 с. Монография посвящена методу функции управляемости, который является развитием метода функции Ляпунова на управляемые системы. Дается применение метода функции управляемости к задаче допустимого синтеза управления для различных классов систем дифференциальных уравнений. Проводится...
Воронеж: ВГУИТ, 2017. — 101 с. Учебное пособие разработано в соответствии с требованиями ФГОС ВО подготовки выпускников по направлению 09.04.02 - «Информационные системы и технологии». Оно предназначено для закрепления теоретических знаний дисциплин цикла Б1. В пособии дан теоретический материал по темам: принципы системной организации, динамические характеристики и параметры...
Систематически изложены методы анализа стохастических процессов и структур в оптике, основанные на фрактальных и мультифрактальных представлениях, а также на возможностях вейвлет-преобразований. Приведены примеры обработки сигналов и оптических изображений. Для студентов и аспирантов, специализирующихся в области физической оптики, оптики лазеров и радиофизики. Учебное пособие....
М.: Наука, 1992. — 256 с. В книге излагаются новые методы решения классических проблем нелинейного анализа: разрешимость, оценка количества решений, применимость приближенных методов, бифуркации, нелинейный резонанс, вариационные принципы и др. Общие результаты применяются для решения важных задач о нелинейных колебаниях в системах управления различных типов, для исследования...
Москва: МГУ им. М.В. Ломоносова, 2007. — 104 с. Изучается простейшая математическая модель, описывающая движение человека на скейтборде. Предполагается, что управление скейтбордом со стороны человека отсутствует. Уравнения движения модели представлены в форме уравнений Гиббса — Аппеля и проведен анализ этих уравнений. Исследуются вопросы интегрируемости полученных уравнений....
Учебное пособие. — Москва: Постмаркет, 2000. — 352 с. Рекомендовано УМО в области электроники и прикладной математики в качестве учебного пособия для студентов по специальности 01.02 «Прикладная математика». Первое полноценное учебное пособие по новой, быстроразвивающейся математической дисциплине - до сих пор на русском языке выходили лишь монографии. Хорошо подобранные...
Саратов: Научная книга, 2010. — 134 с. Представлено введение в теорию дискретных отображений, доступное студентам младших курсов и, в определенной мере, учащимся старших классов. С помощью простых моделей даются понятия о сложной динамике нелинейных систем, в том числе хаосе, бифуркациях, явлении синхронизации. Демонстрируется взаимосвязь и «взаимопомощь» физического и...
Москва; Ижевск: Регулярная и хаотическая динамика, 2006. — 184 с. В сборнике представлено около 450 задач по нелинейным колебаниям, катастрофам, динамическим системам, бифуркациям, хаосу, нелинейным волнам, фракталам и комплексной аналитической динамике. Каждый раздел содержит как теоретические задачи, так и задачи исследовательского характера, решаемые при помощи компьютера....
Цель настоящей брошюры – дать представление о порядке и хаосе в терминах нелинейной динамики. Следует иметь в виду, что нелинейная динамика сейчас это уже и не физика, и не математика, хотя имеет в них глубокие корни и взаимосвязана с ними. Это новая наука, со своими понятиями, терминологией, методами и подходами.
Выходные данные не указаны. Цель настоящей брошюры – дать представление о порядке и хаосе в терминах нелинейной динамики. Следует иметь в виду, что нелинейная динамика сейчас это уже и не физика, и не математика, хотя имеет в них глубокие корни и взаимосвязана с ними. Это новая наука, со своими понятиями, терминологией, методами и подходами. Для широкого круга читателей.
Учебно-методическое пособие для студентов 3 курса факультета нелинейных процессов. — Саратов: СГУ, 2012. — 70 с. Пособие предназначено для использования при проведении семинарских занятий по курсам «Теория катастроф и бифуркаций», «Приложения теории катастроф» у студентов 3 курса факультета нелинейных процессов. Может быть полезно как студентам, изучающим теорию катастроф, так...
Учебно-научное издание. — Саратов: Наука, 2012. — 196 с. — ISBN: 978-5-9999-1185-8. Представлено введение в теорию бифуркаций отображений. Обсуждаются свойства основных бифуркаций. Даны различные примеры. Изложение ведется с «физических» позиций, так что выбираются простейшие модели, для которых проводится комплексное рассмотрение, включая аналитический поиск бифуркаций,...
Саратов: Научная книга, 2010. — 134 с. — ISBN: 978-5-9758-1228-5. Представлено введение в теорию дискретных отображений, доступное студентам младших курсов и, в определенной мере, учащимся старших классов. С помощью простых моделей даются понятия о сложной динамике нелинейных систем, в том числе хаосе, бифуркациях, явлении синхронизации. Демонстрируется взаимосвязь и...
М.: Наука, 1988. — 160 с.
В книге рассмотрены наиболее актуальные вопросы теории и применения нелинейных уравнений, описывающих физические макроскопические процессы. В ней представлены решения уравнений Кортевега — де Фриса, Ван-дер-Поля, синус-Гордона, нелинейных уравнений акустики, газодинамики и магнитной гидродинамики плазмы, электродинамики, уравнений колебаний в мазерных...
М.: Наука, 1988. — 160 с. В книге рассмотрены наиболее актуальные вопросы теории и применения нелинейных уравнений, описывающих физические макроскопические процессы. В ней представлены решения уравнений Кортевега — де Фриса, Ван-дер-Поля, синус-Гордона, нелинейных уравнений акустики, газодинамики и магнитной гидродинамики плазмы, электродинамики, уравнений колебаний в мазерных...
Ростов-на-Дону: ЮФУ, 2009. — 208 с. В монографии изложена общая теория локальных бифуркаций в динамических системах с косимметрией, обладающих в условиях общего положения непрерывным семейством равновесий с. переменным спектром устойчивости. Исследованы бифуркации таких семейств равновесий, которые приводят к рождению вторичных и третичных стационарных режимов, а также...
М.: Наука, Физматлит, 1997. — 496 с. В монографии с единой точки зрения рассмотрены колебательные и волновые процессы в системах самой различной физической природы. Показано, что такие популярные и быстро развивающиеся в последние годы науки, как нелинейная динамика, теория солитонов и синергетика, которые часто изучаются независимо друг от друга, фактически являются составными...
М.: Наука. Физматлит, 1997. — 496 с. В настоящей книге представлено современное состояние теории нелинейных колебаний и волн. С единой точки зрения рассматриваются колебательные и волновые процессы, как периодические, так и хаотические, в системах самой различной физической природы. Показано, что такие популярные и быстро развивающиеся в последние годы науки, как нелинейная...
Учебно-методическое пособие. — Нижний Новгород: Нижегородский госуниверситет, 2015. — 61 с. Динамические системы, представляющие собой математические модели некоторых объектов, процессов или явлений, широко востребованы в различных разделах естествознания. Для изучения сложной динамики таких систем необходимо прежде всего научиться применять методы качественного и численного...
М.: Мир, 1977. — 320 с. Книга представляет собой сборник статей, написанных известными зарубежными физиками и математиками по материалам семинаров, проведенных в Корнеллском университете (США). Статьи содержат доступное изложение идей, лежащих в основе ряда новых направлений в теории нелинейных волн, которая привлекает сейчас большое внимание специалистов самого различного...
М.: Мир, 1985. — 529 с. Монография известных американских физиков, профессоров Калифорнийского университета (Беркли) А. Лихтенберга и М. Либермана посвящена новой быстро развивающейся и малоизвестной области, пограничной между нелинейной механикой и статистической физикой. Основное внимание уделено выяснению физической сущности и механизма, а также условиям возникновения...
М.: Мир, 1985. — 529 с. Монография известных американских физиков, профессоров Калифорнийского университета (Беркли) А. Лихтенберга и М. Либермана посвящена новой быстро развивающейся и малоизвестной области, пограничной между нелинейной механикой и статистической физикой. Основное внимание уделено выяснению физической сущности и механизма, а также условиям возникновения...
Курс лекций для студентов 3 - 5 курсов физического факультета НГУ. — Новосибирск: НГУ, 1977. — 49 с. В курсе лекций с единой точки зрения рассмотрены нелинейные волновые явления в различных ситуациях - при распространении звука и света в сплошной среде, спиновых волн в ферромагнетиках, электромагнитных волн в плазме и т. д. Все эти явления рассмотрены в рамках гамильтоновских...
М.: Мир, 1983. — 294 с. В книге содержится также достаточно полное описание солитонных решений уравнения sine-Gordon и "модифицированного" уравнения КдФ, решениям нелинейного уравнения Шрёдингера и т. д. Лэм Д. Л., из предисловия: "Назначение этой книги - служить элементарным введением в теорию солитонов, предмет, который позволил нам чудесным образом понять внутренний механизм...
М.: Меркурий-Пресс, 2001. — 293 с. Элементарное введение в теорию солитонов - наиболее активно развивающееся направление современной математической физики. Идеи этой теории проникают в различные разделы точных наук - от алгебраической геометрии до астрофизики. Автор - известный американский специалист по математической физике. Книга предназначена для математиков и физиков...
Монография. — Киев: Институт математики НАН Украины, 1999. — 216 с. — (Труды Института математики НАН Украины. Том 28). — ISBN 966-02-1465-0. В книге изложены методы локализации собственных значений матриц и матричных функций, основанные на построении и изучении обобщенного уравнения Ляпунова. Развита теория линейных уравнений и операторов в пространстве матриц. Обобщены...
Ленанд, 2018. — 136 с. Предлагаемый читателю сборник задач предназначен для тех, кто преподает или изучает нелинейную динамику. Он основан на опыте чтения автором ряда курсов, посвященных анализу нелинейных явлений, хаосу, самоорганизации, и проведения семинарских занятий на факультете вычислительной математики и кибернетики МГУ и кафедре прикладной математики и синергетики МФТИ.
2-е изд., испр. — М.: Ленанд, 2018. — 136 с. — (Синергетика: от прошлого к будущему 82; Науку — всем! Шедевры научно-популярной литературы (физика) 148). — ISBN 978-5-9710-4774-2. Предлагаемый читателю сборник задач предназначен для тех, кто преподает или изучает нелинейную динамику. Он основан на опыте чтения автором ряда курсов, посвященных анализу нелинейных явлений, хаосу,...
М.: Эдиториал УРСС, 2000. — 256 с. — ISBN: 5-8360-0132-4. Книга представляет собой введение в нелинейную динамику, синергетику и другие области "нелинейной науки". В ней наводятся мосты между традиционными естественнонаучными дисциплинами, математическими курсами и фундаментальными проблемами, над которыми сейчас работают ученые. Книгу отличает ясное и наглядное изложение...
М.: Эдиториал УРСС, 2000. — 336 с. В книге рассматриваются некоторые ключевые проблемы современной нелинейной динамики. Концепция авторов сводится к тому, что принципиальные трудности, с которыми столкнулся этот междисциплинарный подход, требуют новой парадигмы. В книге сделана попытка наметить ее возможные контуры. На смену эре диссипативных структур и эре динамического хаоса...
М.: Эдиториал УРСС, 2000. — 336 с. В книге рассматриваются некоторые ключевые проблемы современной нелинейной динамики. Концепция авторов сводится к тому, что принципиальные трудности, с которыми столкнулся этот междисциплинарный подход, требуют новой парадигмы. В книге сделана попытка наметить ее возможные контуры. На смену эре диссипативных структур и эре динамического хаоса...
М.: Эдиториал УРСС, 2000. — 336 с. — ISBN 5-8360-0110-3. В книге рассматриваются некоторые ключевые проблемы современной нелинейной динамики. Концепция авторов сводится к тому, что принципиальные трудности, с которыми столкнулся этот междисциплинарный подход, требуют новой парадигмы. В книге сделана попытка наметить ее возможные контуры. На смену эре диссипативных структур и...
Изд. 2-е, исправл. и доп. — М.: Едиториал УРСС, 2002. — 360 с. — (Синергетика: от прошлого к будущему.) — ISBN 5-354-00081-5. В книге рассматриваются некоторые ключевые проблемы современной нелинейной динамики. Концепция авторов сводится к тому, что принципиальные трудности, с которыми столкнулся этот междисциплинарный подход, требуют новой парадигмы. В книге сделана попытка...
Материал учебного пособия посвящён теории динамического хаоса. Рассмотрены способы описания стохастических колебаний детерминированных динамических систем. Проведён анализ различных сценариев перехода к хаосу. Представлены наиболее простые с точки зрения изложения примеры хаотизации движений конкретных динамических систем. Учебное пособие для студентов, обучаемых согласно...
М.: Физматлит, 2001. — 432 с. — ISBN 5-9221-0091-2. Книга содержит обзорные и оригинальные статьи ведущих российских ученых по основным разделам нелинейной механики. Излагаются вопросы составления и анализа уравнений движения механических систем, вопросы корректности основных моделей механики, вопросы интегрируемости и детерминированного хаоса, вопросы устойчивости и теории...
М.: Физматлит, 2001. — 432 с. — ISBN: 5-9221-0091-2. Книга содержит обзорные и оригинальные статьи ведущих российских ученых по основным разделам нелинейной механики. Излагаются вопросы составления и анализа уравнений движения механических систем, вопросы корректности основных моделей механики, вопросы интегрируемости и детерминированного хаоса, вопросы устойчивости и теории...
Тюмень: Вектор-Бук, 2005. — 130 с. В основе современного математического моделирования лежат обыкновенные дифференциальные уравнения, при этом уравнения в частных производных можно рассматривать как их обобщения на бесконечномерные фазовые пространства. Уравнения необходимо составить и найти их решения. В то же время, во многих случаях написать интегрирующееся уравнение...
Учебное пособие. — Челябинск: ЧелГУ, 2015. — 60 с. Излагаются основные понятия теории дискретных динамических систем. Предлагаются задачи по всем разделам. Предназначены для студентов и магистрантов математического факультета. Периодические точки и устойчивые множества Теорема Шарковского Параметризованные семейства и бифуркации Символическая динамика Хаотические функции...
Монография. — М.: Физматлит, 2001. — 272 с. Монография посвящена применению достигнутых результатов нелинейной динамики для построения методологии исследования эволюции. Методологическими средствами демонстрируются возможности преодоления "узких мест" соответствующий конкретно-научных задач благодаря относительно молодым научным дисциплинам: динамической теории информации и...
Монография. — М.: Физматлит, 2001. — 272 с. Монография посвящена применению достигнутых результатов нелинейной динамики для построения методологии исследования эволюции. Методологическими средствами демонстрируются возможности преодоления "узких мест" соответствующий конкретно-научных задач благодаря относительно молодым научным дисциплинам: динамической теории информации и...
Ижевск: Регулярная и хаотическая динамика, 2000. — 320 с. Книга представляет собой вводный курс лекций по голоморфной динамике — одной из интенсивно развивающихся областей современной математики. В них рассмотрена теория римановых поверхностей, теоремы о неподвижной точке. Обсуждаются современные результаты по структуре множеств Жюлиа. Имеется ряд приложений. Предназначена для...
Ижевск: НИЦ «Регулярная и хаотическая динамика», 2000. — 320с. Книга представляет собой вводный курс лекций по голоморфной динамике — одной из интенсивно развивающихся областей современной математики. В них рассмотрена теория римановых поверхностей, теоремы о неподвижной точке. Обсуждаются современные результаты по структуре множеств Жюлиа. Имеется ряд приложений. Предназначена...
Учеб. пособие: В 2 ч. — М.: Изд-во МГТУ им. Н.Э. Баумана, 2008. — 222 с. — ISBN: 978-5-7038-3142-7. Рассмотрены линейные модели управляемых динамических систем в непрерывном времени с сосредоточенными параметрами, представляемые в переменных «вход — выход» и в пространстве состояний: «вход — состояние — выход». Приведены сведения, необходимые для понимания математического...
Киев: Наукова думка, 1971. — 440 с. Книга посвящена изложению метода усреднения, получившего очень широкое применение при решении самых разнообразных задач, связанных с исследованием нелинейных колебательных процессов в физике и технике. В книге излагаются как основополагающие результаты, полученные Н. Н. Боголюбовым в области создания алгоритма и строгого математического...
Киев: Наукова думка, 1971. — 440 с. Книга посвящена изложению метода усреднения, получившего очень широкое применение при решении самых разнообразных задач, связанных с исследованием нелинейных колебательных процессов в физике и технике. В книге излагаются как основополагающие результаты, полученные Н. Н. Боголюбовым в области создания алгоритма и строгого математического...
Киев: Наукова думка, 1987. — 270 с. Книга посвящена развитию метода усреднения Н. Н. Боголюбова на основе использования аппарата непрерывных групп преобразований. Доказываются новые теоремы об асимптотической декомпозиции систем обыкновенных дифференциальных уравнений. Рассматриваются новые классы задач. Основные алгоритмы носят конструктивный характер и сводятся к простейшим...
Монография. — М.: Наука, 1973. — 512 с. Настоящая монография посвящена развитию теории интегральных многообразий (интегральных поверхностей) для различных классов дифференциальных уравнений, встречающихся в нелинейной механике и содержащих «малый» или «большой» параметр. Приведен также анализ структуры решений на многообразиях. Книга должна помочь специалистам, занимающимся...
Монографии. — М: Физматлит, 2010. — 395 c. В монографии предпринимается попытка создания единой теории диссипативных структур Тьюринга-Пригожина для систем параболических и гиперболических уравнений с малой диффузией. Для этого развиваются специальные асимптотические методы исследования проблем существования и устойчивости высокомодовых стационарных режимов в сингулярно...
М.–Ижевск: НИЦ «Регулярная и хаотическая динамика», Ижевский институт компьютерных исследований, 2011. — 356 с. Книга известных ученых Юргена Мозера и Эдуарда Цендера представляет собой введение в теорию динамических систем, в частности, в особый класс гамильтоновых систем. Излагая теоретические основы, авторы стремились использовать простейшие математические методы, а также...
Учебное пособие. — М.: Наука, Физматлит, 1969. — 380 с. Предлагаемая книга возникла из лекций, которые автор читал студентам Московского физико- технического института. Заглавие книги совпадает с названием соответствующего курса, обязательного для студентов, специализирующихся в области прикладной математики. Некоторые вопросы вспомогательного характера. Метод Ляпунова-Пуанкаре....
Учебное пособие. — М.: Наука, Физматлит, 1969. — 380 с. Предлагаемая книга возникла из лекций, которые автор читал студентам Московского физико-технического института. Заглавие книги совпадает с названием соответствующего курса,обязательного для студентов, специализирующихся в области прикладной математики. Для студентов физико-математических специальностей университетов. Автор...
Учеб. пособие. — Самара: Изд - во Самар. гос. аэрокосм. ун-та, 2007. — 160 с. : ил. — ISBN: 978-5-7883-0488-5 Представлено систематическое изложение основных разделов нелинейной динамики. Первая глава представляет собой элементарное введение в теорию динамических систем. Вторая глава подробно знакомит с качественными методами исследования поведения динамических систем в фазовом...
Монография. — М.: Физматлит, 2003. — 208 с. — ISBN 5-9221-0471-3. Монография посвящена разработке и описанию аналитических методов для важного раздела нелинейной физики — теории локализованных волновых процессов. Применение каждого из описываемых методов проиллюстрировано решением конкретных физических проблем. Спектр этих проблем весьма широк. Из них несколько проблем —...
Ред.-сост. И. В. Флоринский. – Электрон. книга. – Пущино: Институт математических проблем биологии РАН, 2013. – 103 с. – ISBN: 978-5-9904237-2-5. В книге впервые публикуется докторская диссертация выдающегося российского математика А. М. Молчанова, защищённая 50 лет назад в период его работы в Отделении прикладной математики Математического института им. В. А. Стеклова АН СССР....
Электронное учебно-методическое пособие. — Нижний Новгород: Нижегородский государственный университет им. Лобачевского Н.И., 2012. — 98 с.
В учебном пособии излагаются методы и приёмы исследования систем обыкновенных дифференциальных уравнений, к которым приводят задачи теории колебаний. Это методы качественной теории и теории бифукаций двумерных динамических систем, метод малого...
Электронное учебно-методическое пособие. — Нижний Новгород: Нижегородский государственный университет им. Лобачевского Н.И., 2012. — 98 с.
В учебном пособии излагаются методы и приёмы исследования систем обыкновенных дифференциальных уравнений, к которым приводят задачи теории колебаний. Это методы качественной теории и теории бифукаций двумерных динамических систем, метод...
Москва-Ижевск: Институт компьютерных исследований, 2003. — 304 стр.
Книга посвящена визуальному представлению и анализу инвариантных множеств для достаточно широкою набора нелинейных динамических систем, к которым приводят задачи из физики, механики, биологии, химии, экономики и др. Для визуализации инвариантных множеств (фазовых кривых, резонансных структур, странных...
Учебно-методическое пособие. – Нижний Новгород: Нижегородский госуниверситет, 2022. — 17 с. Учебно-методическое пособие содержит методы построения решений для набора нелинейных дифференциальных уравнений, играющих фундаментальную роль в теории колебаний. Это уравнения типа Дуффинга, маятниковое уравнение, уравнения Эйлера движения волчка и др. Решения этих уравнений выражаются...
Вводный курс для научных работников и инженеров. — Пер. с англ. Ю. А. Данилова и A.M. Шукурова. — Москва: Мир, 1990. — 311 с. Предлагаемая вниманию читателя книга профессора и декана факультета теоретической и прикладной механики Корнеллского университета Фрэнсиса Муна — заметное явление в довольно обширной литературе по стохастическим колебаниям. Небольшая по объему, она...
Вводный курс для научных работников и инженеров. — Пер. с англ. Ю.А. Данилова и A.M. Шукурова. — Москва: Мир, 1990. — 312 с. Предлагаемая вниманию читателя книга профессора и декана факультета теоретической и прикладной механики Корнеллского университета Фрэнсиса Муна — заметное явление в довольно обширной литературе по стохастическим колебаниям. Небольшая по объему, она...
М.: Наука, 1987. — 424 с.
Излагается новый бурно развивающийся раздел нелинейных колебаний - стохастические и хаотические автоколебания в динамических системах. Исследования этих областей весьма актуально для многих областей науки, позволяет по-новому взглянуть на известные явления, например турбулентность в жидкости, газе и плазме, предсказывать возможность сложного поведения...
Коллектив авторов. — Ярославль: Ярославский государственный университет им. П.Г. Демидова (ЯрГУ), 2013. — 68 с. Ярославский государственный университет им. П.Г. Демидова проводит с 15 по 18 октября 2013 года в г. Ярославле международную конференцию «Нелинейная динамика и её приложения», посвященную 150-летию со дня рождения Поля Пенлеве. Данный сборник содержит тезисы докладов,...
Учебное пособие. — Омск: Омский государственный университет путей сообщения, 2021. — 224 с. — ISBN 9785949412879. Устройства современной техники оснащены нелинейными звеньями различной физической природы – это нелинейное рессорное подвешивание подвижного состава, упругие продольные связи кузова с тележкой, выполненные с предварительным натяжением пружин, демпферы сухого трения,...
Пер. с англ. /Предисл. Б. Б. Кадомцева. — М.: Мир, 1989. — 488 с.
Книга греческого автора посвящена одному из разделов синергетики — развитию общего подхода к исследованию динамики сложных нелинейных систем. Особое внимание уделяется анализу проблемы образования и диссипации той новой информации, которая возникает в процессе развития различных физических и биологических систем....
Учебник. — Пер. с англ. — Предисл. Б. Б. Кадомцева. — М.: Мир, 1989. — 488 с. Книга греческого автора посвящена одному из разделов синергетики— развитию общего подхода к исследованию динамики сложных нелинейных систем. Особое внимание уделяется анализу проблемы образования и диссипации той новой информации, которая возникает в процессе развития различных физических и биологических...
Конспект лекций. — М.: МЭИ, 1980. — 47 с.
В лекциях рассматриваются методы фракционного анализа - приближенного исследования, механических, электромеханических и других систем, описываемых обыкновенными дифференциальными уравнениями.
Фракционный анализ - это область на стыке прикладной математики и инженерии, позволяющая объединить в единую процедуру этапы приближенного...
Монография. — Новосибирск: Наука, 1985. — 318 с. В монографии излагаются результаты нелинейной теории поверхностных и внутренних волн в стратифицированной жидкости. Систематически представлен метод Лагранжа с его апробацией на конкретных примерах. В точной постановке доказаны теоремы существования и единственности решения задачи Коши – Пуассона и существования трехмерной...
Монография. — М.: Наука, 1988. — 192 с. — ISBN: 5-02-006590-0. Излагается принципиально новый подход к описанию и исследованию нелинейных динамических систем, подверженных обобщенным, в частности, импульсным воздействиям. Приводится полное решение вопроса о необходимых условиях слабого экстремума в общей задаче оптимального обобщенного управления со смешанными ограничениями....
Монография. — М.: Наука, 1988. — 192 с. — ISBN: 5-02-006590-0. Излагается принципиально новый подход к описанию и исследованию нелинейных динамических систем, подверженных обобщенным, в частности, импульсным воздействиям. Приводится полное решение вопроса о необходимых условиях слабого экстремума в общей задаче оптимального обобщенного управления со смешанными ограничениями....
СПб.: 2004.
Книга представляет собой вводный курс в конструктивные методы исследования динамических систем. Описаны методы прикладной символической динамики и их применение к изучению неперерывных и дискретных динамических систем. Также рассматриваются методы исследования глобальной структуры динамических систем, основанные на использовании символического образа системы,...
Учебное пособие. — Н.Новгород: ННГУ, 2005. — 78 с. В настоящем пособии описывается явление синхронизации автоколебательных систем (осцилляторов) внешней периодической силой, т.е. явление вынужденной синхронизации. В классической теории синхронизации регулярный (нехаотический) осциллятор, управляемый периодическим сигналом, - главная и исторически первая изученная модель. В пособии...
Учебное пособие для вузов. — М: Высшая школа, 2005. — 326 с.: ил. — ISBN: 5-06-004610-9. Основное внимание уделено раскрытию понятий устойчивости и управляемости динамических систем с позиций современной теории катастроф. Приведены математические методы теорий особенностей и бифуркаций. Дана классификация типов катастроф. Сделано обобщение математических методов теории...
Учебное пособие для вузов. — М: Высшая школа, 2005. — 326 с.: ил. — ISBN: 5-06-004610-9. Основное внимание уделено раскрытию понятий устойчивости и управляемости динамических систем с позиций современной теории катастроф. Приведены математические методы теорий особенностей и бифуркаций. Дана классификация типов катастроф. Сделано обобщение математических методов теории...
М.: Мир, 1993. — 175 c. Книга немецких математиков, посвященная динамике отображений комплексной плоскости и представляющая собой оригинальное введение в теорию нелинейных отображений. Доступное изложение + много красивых иллюстраций.
М.: Мир, 1993.
Книга немецких математиков, посвященная динамике отображений комплексной плоскости и представляющая собой оригинальное введение в теорию нелинейных отображений. Для всех, кто занимается нелинейной динамикой, для всех интересующихся математикой и ее приложениями.
Границы хаоса .
Динамика Ферхьюльста.
Множества Жюлиа и их компьютерное построение.
Классификация...
Таллин: Валгус, 1984. — 156 с. Книга посвящена изложению современного состояния проблемы получения эволюционных уравнений для описания нелинейных волновых процессов в слабодиспергирующих средах. Материал книги разделен на четыре главы. Три главы посвящены изложению методов упрощения в различных ситуациях:, одномерных, слабонеоднородных, волноводных системах. В последней главе...
Монография. — Киев: Институт математики НАН Украины, 2013. — 255 с. — ISBN 966-02-2571-7, 978-966-02-6530-1. В монографии излагается метод инвариантов применительно к классическим функциональным уравнениям. Изучаются как линейные, так и нелинейные уравнения, приводятся типичные примеры. Рассматриваются также дифференциально-функциональные уравнения. Книга рассчитана на...
Учебное пособие. — СПб.: Изд. СПбУ, 1997. — 324 с. В пособии излагаются теоретические основы синергетики, приводятся синергетические методы, используемые при рассмотрении процессов, происходящих в лазерных и молекулярных системах. Выявляются преимущества синергетического подхода - общность описания явлений в разных областях знаний, появление новых математических методов, которые...
СПб.: Изд. СПбУ, 1997. — 324 с. В пособии излагаются теоретические основы синергетики, приводятся синергетические методы, используемые при рассмотрении процессов, происходящих в лазерных и молекулярных системах. Выявляются преимущества синергетического подхода - общность описания явлений в разных областях знаний, появление новых математических методов, которые применяются для...
Книга. Москва - Ижевск: Институт компьютерных исследований, 2002. — 404 с. Эта книга посвящена области исследований, возникшей на стыке двух наук - теории размерности и теории динамических систем. На сегодняшний день это направление оформилось в самостоятельную отрасль науки со своими методами и результатами. Книга дает прекрасное представление о современном этапе ее развития и...
М.: Техносфера, 2003. — 496 c. Явление синхронизации широко распространено в науке, природе, технике и обществе. Тенденция к синхронному поведению наблюдается в столь различных системах, как часы, стрекочущие кузнечики, водители ритма сердца, электронные генераторы, нейроны и аплодирующие зрители. Такие эффекты универсальны, их можно объяснить в рамках единого подхода,...
М: Техносфера, 2003. — 496 c. Явление синхронизации широко распространено в науке, природе, технике и обществе. Тенденция к синхронному поведению наблюдается в столь различных системах, как часы, стрекочущие кузнечики, водители ритма сердца, генерирующие потенциалы действия нейроны и аплодирующие зрители. Такие эффекты универсальны, их можно объяснить в рамках единого подхода,...
М.: Техносфера, 2003. — 496 c. Явление синхронизации широко распространено в науке, природе, технике и обществе. Тенденция к синхронному поведению наблюдается в столь различных системах, как часы, стрекочущие кузнечики, водители ритма сердца, электронные генераторы, нейроны и аплодирующие зрители. Такие эффекты универсальны, их можно объяснить в рамках единого подхода,...
Учебное пособие. — Таганрог: ТРТУ, 2001. — 231 с. Предлагаемое пособие представляет собой расширенный конспект лекций по курсу "Физика. Введение в нелинейную динамику", изучаемому студентами 3-го курса специальности 2101 в 5-м семестре. Основная часть пособия посвящена изложению методов аналитической механики, освоение которых является совершенно необходимым для продвижения в...
Монография. — Саратов: Саратовский государственный университет (СГУ), 2016. — 327 с. В монографии обсуждается моделирование процессов в системах, которые могут быть описаны обыкновенными дифференциальными уравнениями с запаздывающим аргументом как с помощью компьютера, так и методами физического эксперимента. Приводятся результаты поиска полезных приложений полученных...
Учебно-методическое пособие. — Н. Новгород: Нижегородский государственный университет им. Н.И. Лобачевского, 2010. — 93 с. Учебно-методическое пособие включает в себя изложение некоторых задач синтеза и исследования свойств динамического поведения сложных систем с фазовым управлением, реализующих следящую оценку изменяющихся параметров сигналов с амплитудной модуляцией. Задачи...
М.: Всесоюзный НИИ системных исследований, 1982. — 135 с.
Рассматриваются вопросы исследования динамики неоднородных управляемых систем: принципы управления, анализ режимов и устойчивость, идентификация и оптимизация. Особое внимание уделено нелинейным динамическим системам.
Рассматриваются также вопросы анализа макросистем.
Учебное пособие. — Саратов: Саратовский государственный университ им. Н.Г. Чернышевского, 2008. — 133 с.: ил. Данное учебное пособие предназначено для студентов физического факультета, выполняющих лабораторные работы в рамках компьютерного практикума “Методы нелинейной динамики”. Оно содержит описания 9 работ практикума, материал каждой из которых включает постановку задачи,...
М.: Мир, 1980. — 607 с. Монография содержит обзор по теориям особенностей и бифуркаций и их приложениям. Примерно половина книги посвящена математическому аппарату теории, который излагается с самых азов; не предполагаются известными даже простейшие понятия геометрии многообразий и линейной алгебры. Вторую половину занимают приложения - к теории упругости, теории остойчивости...
Монография. — М.: Мир, 1980. — 607 с. Монография содержит обзор по теориям особенностей и бифуркаций и их приложениям. Примерно половина книги посвящена математическому аппарату теории, который излагается с самых азов; не предполагаются известными даже простейшие понятия геометрии многообразий и линейной алгебры. Вторую половину занимают приложения - к теории упругости, теории...
Учебно-методическое пособие. — Нижний Новгород: Нижегородский государственный университет им. Н.И. Лобачевского, 2019. — 33 с. Настоящий сборник задач необходим для студентов и аспирантов, специализирующихся по прикладной математике и информатике, изучающих теорию линейных и в, основном, нелинейных колебаний, устойчивость движения и элементы качественного исследования...
К.: Наукова думка, 1991. — 288 с. Книга посвящена систематическому изложению алгебраических аспектов интегрируемости нелинейных динамических систем на конечно- и бесконечномерных многообразиях. Детально изучена алгебраическая конструкция построения интергируемых по Лиувиллю гамильтоновых динамических систем на однородных пространствах. В области теории интегрируемости динамических...
М.: Наука, 1977. — 256 с.
В книге рассматривается применение метода Пуанкаре к задаче построения периодических решений квазилинейных систем, составленных из дифференциальных уравнений 2-го порядка с аналитическими характеристиками нелинейности.
Книга предназначена для специалистов в теории нелинейных колебаний, а также для аспирантов и студентов университетов и ВТУЗов.
М.: Наука, 1977. – 256 с.
В книге рассматривается применение метода Пуанкаре к задаче построения периодических решений квазилинейных систем, составленных из дифференциальных уравнений 2-го порядка с аналитическими характеристиками нелинейности.
Книга предназначена для специалистов в теории нелинейных колебаний, а также для аспирантов и студентов университетов и ВТУЗов.
М.: Наука, 1976. — 448 с. — (Теоретические основы технической кибернетики). Монография посвящена проблеме кибернетики. Она представляет собой систематическое исследование по теории нелинейных систем, основанное на применении функциональных рядов. Рассматриваются задачи анализа, синтеза и идентификации нелинейных систем. Для их решения используются ряды Вольтерра, многомерные...
М.: Наука, 1976. — 448 с. — (Теоретические основы технической кибернетики). Монография посвящена проблеме кибернетики. Она представляет собой систематическое исследование по теории нелинейных систем, основанное на применении функциональных рядов. Рассматриваются задачи анализа, синтеза и идентификации нелинейных систем. Для их решения используются ряды Вольтерра, многомерные...
Учебное пособие. — Москва: МФТИ, 2014. — 74 с. Пособие посвящено анализу свойств уравнения «реакция–диффузия», базовой математической модели для описания процессов самоорганизации и образования структур в открытых неравновесных системах различной природы. Систематически изложен математический аппарат, основанный на вариационном принципе и градиентной форме уравнения. Изложена...
Москва: Янус-К, 1998. — 192 с. Каким образом на однородной вначале поверхности горизонтального жидкого слоя, находящегося в осциллирующем гравитационном поле, рождаются кристаллические и квазикристаллические пространственные структуры? Почему в двумерном химическом реакторе, где происходит автокаталитичекая реакция, наиболее типичные концентрационные образования — это спирали?...
Москва: Янус-К, 1998. — 192 с. Каким образом на однородной вначале поверхности горизонтального жидкого слоя, находящегося в осциллирующем гравитационном поле, рождаются кристаллические и квазикристаллические пространственные структуры? Почему в двумерном химическом реакторе, где происходит автокаталитичекая реакция, наиболее типичные концентрационные образования — это спирали?...
Учебное пособие. — Екатеринбург: Уральский государственный университет (УГУ) имени А.М. Горького, 2009. — 72 с. — ISBN 978-5-7996-0468-4. В учебном пособии излагаются элементы теории регулярного и стохастического поведения простейших дискретных динамических систем и обсуждаются особенности основных моделей. Предназначено для студентов математических специальностей и...
Екатеринбург: Уральский государственный университет (УГУ) имени А.М. Горького, 2010. — 252 с. — ISBN 978-5-7996-0528-5. Исследуются устойчивость, чувствительность и стабилизация стохастически возмущенных нелинейных динамических систем. Объектом анализа являются стохастические аттракторы - точки покоя, циклы и торы. Значительное внимание уделяется исследованию конкретных...
М.: МЦНМО, 2021. — 224 с. — ISBN 978-5-4439-1622-4. При решении задач теории катастроф широко используются разнообразные методы теории особенностей гладких отображений. Целью данной книги является ознакомление читателей с основными идеями, методами и результатами теории особенностей, а также с её приложениями в теории катастроф (бифуркации положений равновесия динамических...
М.: Лань, 2021. — 168 с. В учебном пособии рассмотрены вопросы, связанные с изучением элементов теории голоморфной динамики — важного раздела современной математики. Голоморфная динамика является компонентом дисциплины — нелинейной динамики. В пособии рассматривается изучение динамики итерированных функций комплексной переменной, исследуется структура неподвижных точек...
М.: Лань, 2018. — 179 с. В настоящем учебном пособии рассмотрены вопросы, связанные с изучением элементов теории дискретных динамических систем — важного раздела современной математики. Данная дисциплина является компонентой математических основ синергетики, находящей приложения в различных областях знаний. В пособии рассматривается построение аттракторов нелинейных отображений в...
Монография. — Иркутск: Иркутский государственный университет (ИГУ), 2013. — 293 с. — ISBN 978-5-9624-0813-2. Излагаются методы анализа интегральных динамических моделей и их приложения. Даны основы теории линейных и нелинейных интегральных уравнений, используемых в моделировании динамических развивающихся систем. Доказаны теоремы существования и единственности гладких и...
Учебное пособие. — Самара: Самарский национальный исследовательский университет (СНИУ) имени академика С.П. Королева, 2022. — 76 с. Пособие написано на основе многолетнего опыта чтения лекций и ведения семинарских занятий. В нем излагается математический аппарат исследования нелинейных динамических систем с быстрыми и медленными переменными, основанный на методе декомпозиции...
Учебно-методическое пособие. — Нижний Новгород: Нижегородский государственный университет (ННГУ) имени Н.И. Лобачевского, 2020. — 38 с. Методические указания предназначены для студентов и специалистов, занимающихся математическим моделированием и исследованием решений и устойчивости динамических систем, описываемых дифференциальными уравнениями с переменными коэффициентами и...
Ижевск: Ижевский институт компьютерных исследований, 2019. — 544 с. В монографии представлено современное состояние теории систем с ограничениями в виде неравенств. Приложения этой теории включают динамику механических систем с ударами и трением, диодные и транзисторные цепи, экономические и транспортные сети, биологические системы с ограничениями ресурсов и пр. Автор вводит...
М.: Мир, 1987. — 76 с. Имя автора хорошо известно советскому читателю по монографии «Теория катастроф», написанной им совместно с Т. Постоном (М.: Мир, 1980). Данная книга посвящена изложению основных положений и практических применений теории катастроф в занимательной форме, чему способствуют многочисленные забавные иллюстрации. Для специалистов, работающих в различных...
М.: Наука, 1986. — 528 с. Посвящается одному из наиболее активно развивающихся направлений современной математической физики — теории солитонов — методу обратной задачи. Приводится полное и систематическое изложение основ метода обратной задачи с гамильтоновой точки зрения, что позволяет связать воедино различные аспекты теории. Основные понятия теории солитонов вначале излагаются...
М.: Наука, 1986. — 528 с. Посвящается одному из наиболее активно развивающихся направлений современной математической физики — теории солитонов — методу обратной задачи. Приводится полное и систематическое изложение основ метода обратной задачи с гамильтоновой точки зрения, что позволяет связать воедино различные аспекты теории. Основные понятия теории солитонов вначале излагаются...
М.: Издательство Физико-Математической литературы, 2002. — 200 с. Рекомендовано Министерством образования Российской Федерации в качестве учебного пособия для студентов высших учебных заведений, обучающихся по физическим специальностям. Книга представляет собой введение в теорию образования структур в далеких от равновесия системах. Читателю предлагается общий взгляд на...
Санкт-Петербург: издательство не указано, 2006. — 377 с. В настоящей книге излагается оригинальный подход к проблеме адаптации в нелинейных динамических системах. Адаптивность как свойство приспособления рассматривается применительно к задачам обработки информации в нелинейных динамических системах, математическая модель которых известна не полностью. В первую очередь теория и...
СПб.: Изд-во ЛКИ, 2006. — 381 с.: ил., табл. — ISBN 978-5-382-00487-7. В настоящей книге излагается оригинальный подход к проблеме адаптации в нелинейных динамических системах. Адаптивность как свойство приспособления рассматривается применительно к задачам обработки информации в нелинейных динамических системах, математическая модель которых известна не полностью. В первую...
М.: Наука, 1994. — 228 с. — ISBN: 5-02-014594-7. Посвящена систематическому исследованию колебаний при внешнем периодическом воздействии в динамических системах с нелинейностями, имеющими разрывы или изломы. Значительное внимание уделено исследованию общей качественной картины возможного поведения систем и ее использованию при решении прикладных задач. На примерах рассмотрения...
Учебно-методическое пособие. — Н. Новгород: Нижегородский государственный университет (ННГУ) имени Н.И. Лобачевского, 2007. — 100 с. В последнее десятилетие в теоретической и математической физике возрос интерес к дискретным бризерам пространственно-локализованным колебательным решениям в нелинейных решеточных системах. Дискретный бризер представляет из себя долгоживущее...
Учебник. — М.: Московский государственный университет (МГУ) имени М.В. Ломоносова, 2018. — 698 с. Учебник содержит систематический материал по основам теории нелинейной динамики сложных систем и её применению в синергетике, кибернетике, информатике, неравновесной термодинамике открытых систем, квантовой механике, кинетике, диффузии (классической и аномальной), диффузионной...
М.: Мир, 1991. — 368 с. Введение. Бифуркации в нелинейных динамических полях. Ветвление состояний равновесия на диаграмме решений. Математические модели. Численные методы и алгоритмы, используемые для анализа нелинейных систем с сосредоточенными параметрами. Численные методы и алгоритмы, используемые для анализа систем с распределенными параметрами.
М.: Мир, 1987. — 400 с.
Книга известных зарубежных ученых В. Хорстхемке (США) и Р. Лефевра (Бельгия) посвящена эффектам, связанным с воздействием внешних шумов на поведение динамических систем различной природы Приводится краткое и ясное изложение основных положений современной математической теории случайных процессов, на которой базируется теория индуцированных шумов...
М.: Мир, 1987. — 400 с. Книга известных зарубежных ученых В. Хорстхемке (США) и Р. Лефевра (Бельгия) посвящена эффектам, связанным с воздействием внешних шумов на поведение динамических систем различной природы Приводится краткое и ясное изложение основных положений современной математической теории случайных процессов, на которой базируется теория индуцированных шумов...
Под. ред. Е.И. Шемякина. — Минск: Технопринт, 2000. — 426 с. — ISBN: 985-6373-69-7. Моделирование стохастических процессов, полей и их вероятностное описание. Математические модели и методы описания структуры неоднородных сред. Статистический вариант метода осреднения для прямой и обратной задач рассеяния в слоистой среде. Распространение волн в упругой среде с дискретными...
М.: Физматлит, 2000. — 296 с. (Второе издание данной книги носит название «Математические модели нелинейной динамики». — М.: Физматлит, 2003. — 296 с.). Обобщаются известные и предлагаются новые методы математического моделирования нелинейных динамических систем. На простых примерах пояснены механизмы возникновения динамического хаоса, самоорганизации и др. Предложен...
М.: Физматлит, 2000. — 296 с. Обобщаются известные и предлагаются новые методы математического моделирования нелинейных динамических систем. На простых примерах пояснены механизмы возникновения динамического хаоса, самоорганизации и др. Предложен принципиально новый подход к моделированию динамических систем, основанный на теории возможностей и нечеткой математике. Он...
2-е изд., испр. — М.: Физматлит, 2003. — 296 с. — ISBN: 5-9221-0366-0. Обобщаются известные и предлагаются новые методы математического моделирования нелинейных динамических систем. На простых примерах пояснены механизмы возникновения динамического хаоса, самоорганизации и др. Предложен принципиально новый подход к моделированию динамических систем, основанный на теории...
2-е изд., испр. — М.: Физматлит, 2003. — 296 с. Обобщаются известные и предлагаются новые методы математического моделирования нелинейных динамических систем. На простых примерах пояснены механизмы возникновения динамического хаоса, самоорганизации и др. Предложен принципиально новый подход к моделированию динамических систем, основанный на теории возможностей и нечеткой...
Учебное пособие. М.-Ижевск: НИЦ "Регулярная и хаотическая динамика", Институт компьютерных исследований, 2011. 164 с. Энтропия как мера хаоса и мультифрактальность как мера порядка рассматриваются как важнейшие универсальные взаимосвязанные и взаимодополняющие понятия, характеризующие сложные системы самой разнообразной природы. Прослежены основные этапы развития этих понятий....
М. – Ижевск: НИЦ «Регулярная и хаотическая динамика», 2011. — 164 с.
Энтропия как мера хаоса и мультифрактальность как мера порядка рассматриваются как важнейшие универсальные, взаимосвязанные и взаимодополняющие понятия, характеризующие сложные системы самой разнообразной природы. Прослежены основные этапы становления и развития этих понятий. Обсуждаются различные варианты...
М.; Ижевск: Институт компьютерных исследований; Регулярная и хаотическая динамика, 2004. — 216 с. — ISBN: 5-93972-296-2. Настоящая книга представляет собой фундаментальный труд по основам нелинейной динамики хаотических и стохастических систем. Книга содержит исчерпывающее введение в теорию динамических и стохастических систем и детальный анализ современных результатов,...
Новосибирск: Наука, Сибирское отделение, 1983. — 160 с. В монографии развивается новый методически простой и удобный вариант статистического подхода к анализу динамических систем, описываемых дифференциальными уравнениями с флуктуирующими параметрами. Подход основан на правилах дифференцирования статистических средних от величин, зависящих от случайного процесса и его предыстории.
Учебное пособие. — Томск: Томский политехнический университет (ТПУ), 2002. — 129 с. Настоящее учебное пособие приготовлено на основе курса лекций, который автор читает на протяжении ряда лет на физическом факультете в Томском государственном университете. В пособии рассмотрен небольшой набор тем, получивших широкое распространение в научной литературе и оказавших значительное...
Учебное пособие. — Томск: Томский политехнический университет (ТПУ), 2002. — 129 с. Настоящее учебное пособие приготовлено на основе курса лекций, который автор читает на протяжении ряда лет на физическом факультете в Томском государственном университете. В пособии рассмотрен небольшой набор тем, получивших широкое распространение в научной литературе и оказавших значительное...
Монография. — К.: Наукова Думка, 1989. — 218 с. Монография посвящена теории одномерных динамических систем — одному из наиболее эффективных методов качественного исследования нелинейных процессов. Изучаются наиболее простые нелинейные отображения интервала, содержащие одну критическую точку, в которых тем не менее представлено почти все многообразие свойств одномерных систем....
Монография. — К.: Наукова Думка, 1989. — 218 с. Монография посвящена теории одномерных динамических систем — одному из наиболее эффективных методов качественного исследования нелинейных процессов. Изучаются наиболее простые нелинейные отображения интервала, содержащие одну критическую точку, в которых тем не менее представлено почти все многообразие свойств одномерных систем....
Учебное пособие. — СПб.: Санкт-Петербургский государственный политехнический университет (СПбПУ), 2010. — 210 с. — ISBN 978-5-7422-1845-6. Приводятся методы анализа нелинейных систем с регулярной и хаотической динамикой. Представлена иерархия свойств динамических систем, вызывающих режим детерминированного хаоса. Рассмотрены численные методы расчета характеристических...
2011. Рассматриваются теоретические и практические аспекты самоподобных, фрактальных и мультифрактальных случайных процессов и разработанные на их основе мультифрактальные модели телекоммуникационного трафика. Приводится всесторонний анализ эффективности функционирования телекоммуникационных сетей в условиях мультифрактального характера трафика. Анализируются теоретические и...
Москва-Ижевск: Институт компьютерных исследований, 2003. - 428 с.
Книга представляет собой наиболее полное руководство по методам нелинейной динамики. В ней обсуждаются вопросы структурной устойчивости, теория бифуркаций, инвариантные торы и теоремы о центральном многообразии. Наряду с классическими результатами в ней обсуждаются новые методы, в основном созданные нижегородской...
Москва-Ижевск: Институт компьютерных исследований, 2003. - 428 с. Книга представляет собой наиболее полное руководство по методам нелинейной динамики. В ней обсуждаются вопросы структурной устойчивости, теория бифуркаций, инвариантные торы и теоремы о центральном многообразии. Наряду с классическими результатами в ней обсуждаются новые методы, в основном созданные нижегородской...
М.; Ижевск: Регулярная и хаотическая динамика, Институт компьютерных исследований, 2009. — 548 с. — ISBN: 978-5-93972-700-6. Книга представляет собой полное руководство по качественным методам теории динамических систем и теории бифуркаций в нелинейной динамике. В ней обсуждаются вопросы структурной устойчивости, теория локальных и гомоклинических бифуркаций, инвариантные торы...
М.: Мир, 1979. — 279 с. Книга представляет собой введение в теорию возникновения структур при необратимых процессах. На простых примерах из физики, химии и биологии автор знакомит читателя с основными идеями и результатами теории, формулирует общие законы, которым подчиняются процессы, протекающие в самых различных системах. Рассчитана на широкий круг читателей - физиков, химиков,...
Москва; Ижевск: Институт компьютерных исследований, 2003. — 248 с. — ISBN 593972289X. Книга представляет собой введение в теорию возникновения структур при необратимых процессах. На простых примерах из физики, химии и биологии автор знакомит читателя с основными идеями и результатами теории, формулирует общие законы, которымп одчиняются процессы, протекающие в самых различных...
М.: Мир, 1979. — 279 с. Книга представляет собой введение в теорию возникновения структур при необратимых процессах. На простых примерах из физики, химии и биологии автор знакомит читателя с основными идеями и результатами теории, формулирует общие законы, которым подчиняются процессы, протекающие в самых различных системах. Рассчитана на широкий круг читателей - физиков,...
Учебное пособие. — СПб.: Лань, 2015. — 272 c. — (Учебники для вузов. Специальная литература). Основная цель пособия — дать по возможности целостное представление о предмете и методах общей теории динамических систем. В пособии приводятся элементарные сведения из общей теории динамических систем, рассматриваются некоторые вопросы нелинейной динамики, теории локальных бифуркаций....
Учебное пособие. — СПб.: Лань, 2015. — 272 c. — (Учебники для вузов. Специальная литература). Основная цель пособия — дать по возможности целостное представление о предмете и методах общей теории динамических систем. В пособии приводятся элементарные сведения из общей теории динамических систем, рассматриваются некоторые вопросы нелинейной динамики, теории локальных бифуркаций....
Спасибо, отличный раздел, только книга "Гамильтонов хаос и фрактальная динамика" Заславского имелась бы и вообще замечательно было, а то нигде найти не могу...
Я так думаю что это всё таки физика Математика здесь лишь язык. Поэтому думаю надо перенести в физику. Поскольку законами мира занимается физика. Устойчивость, наблюдаемость, управляемость, стохастичность, хотя и имеют выражения в других науках, это физические категории. Биофизика, Эконофизика, Химфизика, Нелинейная Физика Системная Физика. И т.д.
Не согласен. Если геометрия началась с измерения участков земли это не повод ее относить к геологическим дисциплинам. Нелинейные динамические системы - это математические абстракции, не вижу смысла их ограничивать лишь "физическим" применением.
Обалдеть! Наконец-то появился этот раздел! Ждала целый год! Теперь будем собирать инфу для того, чтобы получить Нелинейную динамику в экономике!Супер! Спасибо Вдохновителям и Создателям!
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Поскольку законами мира занимается физика. Устойчивость, наблюдаемость, управляемость, стохастичность, хотя и имеют выражения в других науках, это физические категории.
Биофизика,
Эконофизика,
Химфизика,
Нелинейная Физика
Системная Физика.
И т.д.
Если геометрия началась с измерения участков земли это не повод ее относить к геологическим дисциплинам.
Нелинейные динамические системы - это математические абстракции, не вижу смысла их ограничивать лишь "физическим" применением.
Теперь будем собирать инфу для того, чтобы получить Нелинейную динамику в экономике!Супер! Спасибо Вдохновителям и Создателям!