New Methods for Chaotic Dynamics

New Methods for Chaotic Dynamics
Author: Nikolai Aleksandrovich Magnitskii
Publisher: World Scientific
Total Pages: 382
Release: 2006
Genre: Mathematics
ISBN: 9812773517


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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. Sample Chapter(s). Chapter 1: Systems of Ordinary Differential Equations (1,736 KB). 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.


New Methods for Chaotic Dynamics
Language: en
Pages: 382
Authors: Nikolai Aleksandrovich Magnitskii
Categories: Mathematics
Type: BOOK - Published: 2006 - Publisher: World Scientific

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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-d
New Methods for Chaotic Dynamics
Language: en
Pages: 382
Authors: Nikola? Aleksandrovich Magnit?ski?
Categories: Science
Type: BOOK - Published: 2006 - Publisher: World Scientific

GET EBOOK

"An improved realization of mixed-mode chaotic circuit which has both autonomous and nonautonomous chaotic dynamics is proposed. Central to this study is induct
Chaotic Dynamics
Language: en
Pages: 282
Authors: Gregory L. Baker
Categories: Science
Type: BOOK - Published: 1996 - Publisher: Cambridge University Press

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The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely
Chaotic Dynamics
Language: en
Pages: 368
Authors: Alfredo Medio
Categories: Business & Economics
Type: BOOK - Published: 1992 - Publisher: Cambridge University Press

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The modelling of economic models by means of dynamic systems.
Recent Trends In Chaotic, Nonlinear And Complex Dynamics
Language: en
Pages: 561
Authors: Jan Awrejcewicz
Categories: Science
Type: BOOK - Published: 2021-07-26 - Publisher: World Scientific

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In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances mad