Main Data
Author: Vadim S. Anishchenko, Vladimir Astakhov, Alexander Neiman, Tatjana Vadivasova, Lutz Schimansky-Geier
Title: Nonlinear Dynamics of Chaotic and Stochastic Systems Tutorial and Modern Developments
Publisher: Springer-Verlag
ISBN/ISSN: 9783540381686
Edition: 2
Price: CHF 98.50
Publication date: 01/01/2007
Category: Wirtschaft/Management
Language: English
Technical Data
Pages: 446
Kopierschutz: DRM
Geräte: PC/MAC/eReader/Tablet
Formate: PDF
Table of contents
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.
Table of contents
Preface to the Second Edition7
Preface to the First Edition8
1. Tutorial15
1.1 Dynamical Systems15
1.2 Fluctuations in Dynamical Systems51
1.3 Synchronization of Periodic Systems94
2. Dynamical Chaos123
2.1 Routes to Chaos123
2.2 Statistical Properties of Dynamical Chaos153
2.3 Synchronization of Chaos178
2.4 Effects of Synchronization in Extended Self- Sustained Oscillatory Systems199
2.5 Synchronization in Living Systems239
2.6 Controlling Chaos247
2.7 Reconstruction of Dynamical Systems278
3. Stochastic Dynamics321
3.1 Stochastic Resonance321
3.2 Synchronization of Stochastic Systems365
3.3 The Beneficial Role of Noise in Excitable Systems395
3.4 Noise-Induced Transport413