NEW METHODS FOR CHAOTIC DYNAMICS: 58 (WORLD SCIENTIFIC SERIES ON NONLINEAR SCIENCE SERIES A) - Hardcover

Magnitskii, Nikolai Alexandrovich; Sidorov, Sergey Vasilevich

Hardcover

ISBN 10: 9812568174 ISBN 13: 9789812568175

Publisher: World Scientific Publishing Co Pte Ltd, 2006

Synopsis

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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Review

Bringing new interesting ideas, this monograph is a valuable contribution to the existing literature on the subject
-- Zentralblatt MATH

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 2006
• Language: English
• ISBN 10: 9812568174
• ISBN 13: 9789812568175
• Binding: Hardcover
• Number of pages: 384