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Chaos : concepts, control and constructive use

Author: Yurii Bolotin; Anatoli Tur; Vladimir Yanovsky
Publisher: Dordrecht ; New York : Springer, ©2009.
Series: Understanding complex systems.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

With an emphasis on controlled and constructive chaos, this concise primer for postgraduates skillfully leads the reader through the algorithms of chaos control, and then tackles synchronization in  Read more...

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Document Type: Book
All Authors / Contributors: Yurii Bolotin; Anatoli Tur; Vladimir Yanovsky
ISBN: 3642009360 9783642009365
OCLC Number: 429183618
Description: viii, 198 pages : illustrations ; 25 cm.
Contents: 1 Introduction 1 --
2 Paradigm for Chaos 5 --
2.1 Order and Disorder 6 --
2.2 Algorithms and the Turing Machine 8 --
2.3 Complexity and Randomness 11 --
2.4 Chaos in a Simple Dynamical System 14 --
3 Main Features of Chaotic Systems 19 --
3.1 Poincare Sections 19 --
3.2 Spectral Density and Correlation Functions 21 --
3.3 Lyapunov's Exponent 25 --
3.4 Invariant Measure 32 --
4 Reconstruction of Dynamical Systems 35 --
4.1 What Is Reconstruction? 35 --
4.2 Embedding Dimension 38 --
4.3 Attractor Dimension 41 --
4.4 Finding the Embedding Dimension 47 --
4.5 Global Reconstruction of Dynamical Systems 50 --
5 Controlling Chaos 51 --
5.1 Statement of the Problem 51 --
5.2 Discrete Parametric Control and Its Strategy 52 --
5.3 Main Equations for Chaos Control 56 --
5.4 Control of Chaos Without Motion Equations 61 --
5.5 Targeting Procedure in Dissipative Systems 65 --
5.6 Chaos Control in Hamiltonian Systems 67 --
5.7 Stabilization of the Chaotic Scattering 70 --
5.8 Control of High-Periodic Orbits in Reversible Mapping 73 --
5.9 Controlling Chaos in a Time-Dependant Irregular Environment 78 --
5.10 Continuous Control with Feedback 80 --
5.11 Can Quantum Dynamics Be Controlled? 91 --
6 Synchronization of Chaotic Systems 101 --
6.1 Statement of Problem 102 --
6.2 Geometry and Dynamics of the Synchronization Process 103 --
6.3 General Definition of Dynamical System Synchronization 106 --
6.4 Chaotic Synchronization of Hamiltonian Systems 108 --
6.5 Realization of Chaotic Synchronization Using Control Methods 111 --
6.6 Synchronization Induced by Noise 117 --
6.7 Synchronization of Space-Temporal Chaos 122 --
6.8 Additive Noise and NonIdentity Systems Influence on Synchronization Effects 125 --
6.9 Synchronization of Chaotic Systems and Transmission of Information 129 --
7 Stochastic Resonance 135 --
7.1 Qualitative Description of the Effect 135 --
7.2 The Interaction Between the Particle and its Surrounding Environment 138 --
7.3 The Two-States Model 142 --
7.4 Stochastic Resonance in Chaotic Systems 149 --
7.5 Stochastic Resonance and Global Change in the Earth's Climate 153 --
8 The Appearance of Regular Fluxes Without Gradients 159 --
8.1 Introduction 159 --
8.2 Dynamical Model of the Ratchet 163 --
8.3 Ratchet Effect-an Example of Real Realization 168 --
8.4 Principal Types of Ratchets 171 --
8.5 Nonlinear Friction as the Mechanism of Directed Motion Generation 176 --
8.6 Change of Current Direction in the Deterministic Ratchet 182 --
8.7 Bio or Molecular Motors 185.
Series Title: Understanding complex systems.
Responsibility: Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky.

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From the reviews: "This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems in order to reach a large audience from science and engineering. The Read more...

 
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