Nonlinear Dynamics of Chaotic and Stochastic Systems

Author: Vadim S. Anishchenko
Publisher: Springer Science & Business Media
ISBN: 3540381686
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We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

Nonlinear Dynamics in Circuits

Author: Thomas L. Carroll
Publisher: World Scientific
ISBN: 9789810224387
Format: PDF, ePub, Mobi
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This volume describes the use of simple analog circuits to study nonlinear dynamics, chaos and stochastic resonance. The circuit experiments that are described are mostly easy and inexpensive to reproduce, and yet these experiments come from the forefront of nonlinear dynamics research. The individual chapters describe why analog circuits are so useful for studying nonlinear dynamics, and include theoretical as well as experimental results from some of the leading researchers in the field. Most of the articles contain some tutorial sections for the less experienced readers.The audience for this book includes researchers in nonlinear dynamics, chaos and statistical physics as well as electrical engineering, and graduate and advanced undergraduate students in these fields.

Chaos Fractals and Noise

Author: Andrzej Lasota
Publisher: Springer Science & Business Media
ISBN: 146124286X
Format: PDF, Mobi
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The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.

Nonlinear Dynamics and Stochastic Mechanics

Author: Wolfgang Kliemann
Publisher: American Mathematical Soc.
ISBN: 0821802577
Format: PDF
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This volume contains the proceedings of the International Symposium on Nonlinear Dynamics and Stochastic Mechanics held at The Fields Institute for Research in Mathematical Sciences from August-September (1993) as part of the 1992-1993 Program Year on Dynamical Systems and Bifurcation Theory. In recent years, mathematicians and applied scientists have made significant progress in understanding and have developed powerful tools for the analysis of the complex behavior of deterministic and stochastic dynamical systems. By moving beyond classical perturbation methods to more general geometrical, computational, and analytical methods, this book is at the forefront in transferring these new mathematical ideas into engineering practice. This work presents the solutions of some specific problems in engineering structures and mechanics and demonstrates by explicit example these new methods of solution. Features: Joins problems in engineering science to recent developments in the mathematical theory of dynamical systems. Offers novel applications of dynamical systems theory. Presents numerical methods for stochastic systems. Compares analytical and numerical studies near the onset of chaos. In one volume, brings together and contrasts deterministic and stochastic models of ``chaos''.

Nonlinear Dynamics in Engineering Systems

Author: Werner Schiehlen
Publisher: Springer Science & Business Media
ISBN: 3642835783
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The International Union of Theoretical and Applied Mechanics (IUTAM) initiated and sponsored an International Symposium on Nonlinear Dynamics in Engineering Systems held in 1989 in Stuttgart, FRG. The Symposium was intended to bring together scientists working in different fields of dynamics to exchange ideas and to discuss new trends with special emphasis on nonlinear dynamics in engineering systems. A Scientific Committee was appointed by the Bureau of IUTAM with the following members: S. Arimoto (Japan), F.L. Chernousko (USSR), P.J. Holmes (USA), C.S. Hsu (USA), G. looss (France), F.C. Moon (USA), W. Schiehlen (FRG), Chairman, G. Schmidt (GDR), W. Szemplinska-Stupnicka (Poland), J.M.T. Thompson (UK), H. Troger (Austria). This committee selected the participants to be invited and the papers to be presented at the Symposium. As a result of this procedure 78 active scientific participants from 22 countries followed the invitation, and 44 papers were presented in lecture and poster sessions. They are collected in this volume. At the Symposium an exhibition with experiments took place and the movie "An Introduction to the Analysis of Chaotic Dynamics" by E.J. Kreuzer et.al. was presented. The scientific lectures were devoted to the following topics: o Dynamic Structural Engineering Problems, o Analysis of Nonlinear Dynamic Systems, o Bifurcation Problems, o Chaotic Dynamics and Control Problems, o Miscellaneous Problems, o Experimental and Theoretical Investigations, o Chaotic Oscillations of Engineering Systems, o Characterization of Nonlinear Dynamic Systems, o Nonlinear Stochastic Systems.

Nonlinear Dynamics and Chaos Advances and Perspectives

Author: Marco Thiel
Publisher: Springer
ISBN: 3642046290
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This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.

Stochastic Non Excitable Systems with Time Delay

Author: Paul M. Geffert
Publisher: Springer
ISBN: 3658092955
Format: PDF
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Paul M. Geffert analyses the interplay of noise and time delay in non-excitable nonlinear systems and the modulation of stochastic effects. In particular, the author studies coherence resonance, which is a constructive effect of noise that occurs in nonlinear systems, and demonstrates that it can be modulated by time-delayed feedback. Analytical methods for the investigation of stochastic delay differential equations are developed. Noise or random perturbations and time delay are two phenomena which arise in many fields of physics, chemistry, or biology, just to mention a few examples. The investigated model is a generic Hopf normal form so that these methods and results can be transferred to many different areas of science.

Regular and Chaotic Dynamics

Author: Allan Lichtenberg
Publisher: Springer Science & Business Media
ISBN: 1475721846
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This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.

Chaos And Nonlinear Mechanics Proceedings Of Euromech Colloquium 308 Chaos And Noise In Dynamical Systems

Author: Kapitaniak Tomasz
Publisher: World Scientific
ISBN: 9814550213
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This volume contains a selection of papers presented at Euromech Colloquium 308 — Chaos and Noise in Dynamical Systems.Roughly speaking, a chaotic solution to an ordinary differential equation is aperiodic and “looks like” a stochastic process. On the other hand, the theory of probability and stochastic processes was developed to describe complicated irregular phenomena taking place in the real world, which in most cases are chaotic. This observation led to the idea of bringing together experts on both nonlinear chaotic and stochastic systems for the conference. Equal attention was given to recent theoretical results and practical applications.The revised and updated papers in this volume are grouped in the following sections: Theory of Chaotic Systems; Stochastic Systems; Spatiotemporal Systems and Fluid Dynamics; Numerical Tools; and Practical Applications. Each section starts with a short introduction and a brief summary of the presented papers.