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 deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems.
This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Author(s): Vadim S. Anishchenko, Tatyana E. Vadivasova, Galina I. Strelkova (auth.)
Series: Springer Series in Synergetics
Edition: 1
Publisher: Springer International Publishing
Year: 2014
Language: English
Pages: 294
Tags: Nonlinear Dynamics; Classical Continuum Physics; Vibration, Dynamical Systems, Control; Mathematical Applications in the Physical Sciences
Front Matter....Pages i-xiv
Dynamical Systems....Pages 1-22
Stability of Dynamical Systems: Linear Approach....Pages 23-35
Bifurcations of Dynamical Systems....Pages 37-52
Dynamical Systems with One Degree of Freedom....Pages 53-73
Systems with Phase Space Dimension N ≥ 3: Deterministic Chaos....Pages 75-92
From Order to Chaos: Bifurcation Scenarios (Part I)....Pages 93-105
From Order to Chaos: Bifurcation Scenarios (Part II)....Pages 107-122
Robust and Nonrobust Dynamical Systems: Classification of Attractor Types....Pages 123-143
Characteristics of Poincaré Recurrences....Pages 145-156
Fractals in Nonlinear Dynamics....Pages 157-173
The Anishchenko–Astakhov Oscillator of Chaotic Self-Sustained Oscillations....Pages 175-201
Quasiperiodic Oscillator with Two Independent Frequencies....Pages 203-215
Synchronization of Periodic Self-Sustained Oscillations....Pages 217-243
Synchronization of Two-Frequency Self-Sustained Oscillations....Pages 245-271
Synchronization of Chaotic Oscillations....Pages 273-294
