A01=Nikolai Alexandrovich Magnitskii
A01=Sergey Vasilevich Sidorov
Author_Nikolai Alexandrovich Magnitskii
Author_Sergey Vasilevich Sidorov
Cascades of Bifurcations
Category=PHDS
Chaos Control
Dynamical Chaos
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Nonlinear Differential Equations
Scenarios of Transition to Chaos
Spatio-Temporal Chaos
Product details
- ISBN 9789812568175
- Publication Date: 05 Oct 2006
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
