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World Scientific Series on Nonlinear Science, Series A - Vol. 58

NEW METHODS FOR CHAOTIC DYNAMICS

by Nikolai Alexandrovich Magnitskii & Sergey Vasilevich Sidorov (Russian Academy of Sciences, Russia)

Table of Contents (195k)
Preface (204k)
Chapter 1: Systems of Ordinary Differential Equations (1,736k)

This book presents a new theory on the transition to dynamical chaos for two-dimensional nonautonomous, and three-dimensional, many-dimensional and infinitely-dimensional autonomous nonlinear dissipative systems of differential equations including nonlinear partial differential equations and differential equations with delay arguments.

The transition is described from the Feigenbaum cascade of period doubling bifurcations of the original singular cycle to the complete or incomplete Sharkovskii subharmonic cascade of bifurcations of stable limit cycles with arbitrary period and finally to the complete or incomplete homoclinic cascade of bifurcations.

The book presents a distinct view point on the principles of formation, scenarios of occurrence and ways of control of chaotic motion in nonlinear dissipative dynamical systems. All theoretical results and conclusions of the theory are strictly proved and confirmed by numerous examples, illustrations and numerical calculations.


Contents:

  • Systems of Ordinary Differential Equations
  • Bifurcations in Nonlinear Systems of Ordinary Differential Equations
  • Chaotic Systems of Ordinary Differential Equations
  • Principles of the Theory of Dynamical Chaos in Dissipative Systems of Ordinary Differential Equations
  • Dynamical Chaos in Infinitely-Dimensional Systems of Differential Equations
  • Chaos Control in Systems of Differential Equations


Readership: Graduate students and researchers in complex and chaotic dynamical systems.


“Bringing new interesting ideas, this monograph is a valuable contribution to the existing literature on the subject.”

Zentralblatt MATH




384pp Pub. date: Oct 2006
ISBN 978-981-256-817-5
981-256-817-4
US$77 / £39


Copyright © 2008 World Scientific Publishing Co. All rights reserved.
Updated on 4 July 2008