Deterministic Nonlinear Systems

A Short Course

Vadim S. Anishchenko, Tatyana E. Vadivasova, Galina I. Strelkova

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English

Springer International Publishing AG
07 July 2014

Mathematical modelling; Non-linear science; Classical mechanics; Dynamics & vibration

Series: Springer Series in Synergetics

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.

By: Vadim S. Anishchenko, Tatyana E. Vadivasova, Galina I. Strelkova
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2015 ed.
Dimensions: Height: 235mm, Width: 155mm, Spine: 19mm
Weight: 5.856kg
ISBN: 9783319068701
ISBN 10: 3319068709
Series: Springer Series in Synergetics
Pages: 294
Publication Date: 07 July 2014
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

From the Contents: Part I Dynamical Systems.- Stability of Dynamical Systems.- Linear Approach.- Bifurcations of Dynamical Systems.- Dynamical Systems With One Degree of Freedom.- 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.- The Anishchenko–Astakhov Oscillator of Chaotic Self-Sustained Oscillations.- Quasiperiodic Oscillator with Two Independent Frequencies.- Synchronization of Periodic Self-Sustained Oscillations.- Synchronization of Two-Frequency Self-Sustained Oscillations.-Synchronization of Chaotic Oscillations.- References.

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.