New Methods For Chaotic Dynamics

By: Sergey Vasilevich Sidorov, Nikolai Alexandrovich Magnitskii

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Hardcover | 5 October 2006

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384 Pages

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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.

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Systems of ordinary differential equations	p. 1
Bifurcations in nonlinear systems of ordinary differential equations	p. 45
Chaotic systems of ordinary differential equations	p. 107
Principles of the theory of dynamical chaos in dissipative systems of ordinary differential equations	p. 191
Dynamical chaos in infinite-dimensional systems of differential equations	p. 261
Chaos control in systems of differential equations	p. 309
Table of Contents provided by Blackwell. All Rights Reserved.

New Methods For Chaotic Dynamics

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