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Author Wu, Chai Wah.

Title Synchronization in coupled chaotic circuits and systems [electronic resource] / Chai Wah Wu.

Imprint River Edge, N.J. : World Scientific, ©2002.

Item Status

Description 1 online resource (xi, 174 pages) : illustrations.
Series World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 41
World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 41.
Bibliography Includes bibliographical references (pages 165-172) and index.
Contents Preface; Contents; Chapter 1 Introduction; Chapter 2 Synchronization in Two Coupled Chaotic Systems; 2.1 Pecora-Carroll subsystem decomposition; 2.2 Separable additive coupling; 2.3 Synchronization and stability; 2.3.1 Absolute stability; 2.3.2 Lipschitz nonlinear systems; 2.3.3 Circuit theoretical criteria for asymptotical stability; 2.4 Communication and signal processing via synchronization of chaotic systems; 2.5 Synchronization of nonautonomous systems; 2.5.1 Unidirectional synchronization scheme for nonautonomous systems.
2.5.2 Mutual coupling synchronization scheme for nonautonomous systems2.5.3 Synchronization between different systems; 2.5.4 Synchronizing nonautonomous systems as communication systems; 2.6 Synchronization via a scalar signal; 2.6.1 Applications of scalar synchronization to chaotic communication system; 2.7 Adaptive synchronization; 2.7.1 A general adaptive scheme; 2.7.2 Two coupled nonlinear systems with linear parameters; 2.7.3 Two coupled nonlinear systems with multiplicative parameters; 2.7.4 Examples; 2.7.5 A generalization of the scheme in Eq. (2.35); 2.7.6 Adaptive observers.
2.8 Discrete-time systems2.9 Further reading; Chapter 3 Synchronization in Coupled Arrays of Chaotic Systems; 3.1 Uniform linear static coupling; 3.1.1 G is normal; 3.1.2 G is symmetric; 3.1.3 General G; 3.2 Uniform nonlinear static coupling; 3.3 From stability results to synchronization criteria in coupled arrays; 3.4 Discrete-time systems; Chapter 4 Synchronization in Coupled Arrays: Dynamic Coupling; 4.1 Synchronization of clusters; 4.2 Regular and uniform hypergraphs in linearly coupled arrays; 4.3 Two identical systems coupled by dynamic coupling.
Chapter 5 Graph Topology and Synchronization5.1 Some coupling configurations; 5.2 Continuous time systems; 5.3 Discrete-time systems; 5.4 Graph coloring via synchronized array of coupled oscillators; 5.4.1 Coloring two-colorable graphs; 5.4.2 Coloring arbitrary graphs; 5.4.3 Antivoter model for graph coloring; 5.4.4 Calculating the star chromatic number of a graph; Chapter 6 Lyapunov Exponents Approach to Synchronization; 6.1 Continuous-time systems; 6.2 Discrete-time systems; 6.3 Three oscillator universal probe for determining synchronization in coupled arrays.
Appendix A Some Linear Systems Theory and Matrix TheoryAppendix B Graph Theoretical Definitions and Notations; Appendix C Stability Lyapunov's Direct Method and Lyapunov Exponents; C.l Lyapunov function and Lyapunov's direct or second method; C.2 Lyapunov exponents; Appendix D Chaotic Circuits and Systems; D.l Nonautonomous chaotic circuits and systems; D.l.l Circuit 1; D.1.2 Circuit 2; D.2 Autonomous chaotic circuits and systems; D.2.1 Chua's oscillator; D.2.2 Piecewise-linear Rossler system; D.2.3 Hyperchaotic electronic circuit; D.2.4 Hyperchaotic Rossler system; Bibliography; Index.
Summary This invaluable book studies synchronization of coupled chaotic circuits and systems, as well as its applications. It shows how one can use stability results in nonlinear control to derive synchronization criteria for coupled chaotic circuits and systems. It also discusses the use of Lyapunov exponents in deriving synchronization criteria. Both the case of two coupled systems and the case of arbitrarily coupled arrays of systems are considered. The book examines how synchronization properties in arrays of coupled systems are dependent on graph-theoretical properties of the underlying coupling.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Electronic circuits.
Chaotic behavior in systems.
Coupled mode theory.
Genre/Form Electronic books.
Other Form: Print version: Wu, Chai Wah. Synchronization in coupled chaotic circuits and systems. River Edge, N.J. : World Scientific, ©2002 (DLC) 2002279811
ISBN 9789812778420 (electronic bk.)
981277842X (electronic bk.)