Deterministic Nonlinear Systems

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.

Auteur

Prof. Dr. Vadim S. Anishchenko is Head of Radiophysics and Nonlinear Dynamics Chair and the scientific supervisor of the Laboratory of Nonlinear Dynamics of Saratov State University. He is a specialist in the field of theory of oscillations, statistical radiophysics and nonlinear dynamics and the author of seven scientific monographs, three text-books and of more than 200 journal articles.

Prof. Anishchenko is an Honored Man of Sciences of Russia, a corresponding member of Russian Academy of Natural Sciences, and Soros Professor. In 1999 he was elected the recipient of a Humboldt Research Award.

Contenu

3, Deterministic Chaos.- From Order to Chaos: Bifurcation Scenarios.- Part II From Order to Chaos: Bifurcation Scenarios.- Robust and Nonrobust Dynamical Systems. Classification of Attractor Types.- Characteristics of Poincare Recurrences.- Fractals in Nonlinear Dynamics.- Anishchenko - Astakhov Oscillator of Chaotic Self-sustained Oscillations.- Oscillator of Two-Frequency Quasiperiodic Oscillations.- Synchronization of Periodic Self-sustained Oscillations.- Synchronization of Two-frequency Self-sustained Oscillations.- Synchronization of Chaotic Oscillations.- Recommended Literature.