Synchronization in coupled chaotic circuits and systems (World Scientific series on nonlinear science. Series A, Monographs and treatises; v. 41)

Cover\r......Page 1
Series Info\r......Page 3
Synchronization in Coupled Chaotic Circuits and Systems\r......Page 4
Copyright\r......Page 5
Preface......Page 8
Contents......Page 10
1 Introduction......Page 14
2 Synchronization in Two Coupled Chaotic Systems......Page 16
2.2 Separable additive coupling......Page 19
2.3 Synchronization and stability......Page 20
2.3.1 Absolute stability......Page 21
2.3.2 Lipschitz nonlinear systems......Page 23
2.3.3 Circuit theoretical criteria for asymptotical stability......Page 24
2.4 Communication and signal processing via synchronization of chaotic systems......Page 26
2.5 Synchronization of nonautonomous systems......Page 31
2.5.1 Unidirectional synchronization scheme for nonautonomous systems......Page 32
2.5.2 Mutual coupling synchronization scheme for nonautonomous systems......Page 33
2.5.3 Synchronization between different systems......Page 35
2.5.4 Synchronizing nonautonomous systems as communication systems......Page 37
2.6 Synchronization via a scalar signal......Page 40
2.6.1 Applications of scalar synchronization to chaotic communication system......Page 45
2.7 Adaptive synchronization......Page 46
2.7.1 A general adaptive scheme......Page 48
2.7.2 Two coupled nonlinear systems with linear pammeters......Page 49
2.7.3 Two coupled nonlinear systems with multiplicative parameters......Page 53
2.7.4 Examples......Page 55
2.7.5 A genemliaation of the scheme in Eq. (2.35)......Page 58
2.7.6 Adaptive observers......Page 59
2.8 Discrete-time systems......Page 61
2.9 Further reading......Page 62
3 Synchronization in Coupled Arrays of Chaotic Systems......Page 64
3.1 Uniform linear static coupling......Page 68
3.1.1 G is normal......Page 71
3.1.2 G is symmetric......Page 73
3.1.3 Geneml G......Page 74
3.2 Uniform nonlinear static coupling......Page 78
3.3 From stability results to synchronization criteria in coupled arrays......Page 80
3.4 Discrete-time systems......Page 83
4 Synchronization in Coupled Arrays: Dynamic Coupling......Page 90
4.1 Synchronization of clusters......Page 94
4.2 Regular and uniform hypergraphs in linearly coupled arrays......Page 101
5 Graph Topology and Synchronization......Page 112
5.1 Some coupling configurations......Page 113
5.2 Continuous time systems......Page 116
5.3 Discrete-time systems......Page 120
5.4 Graph coloring via synchronized array of coupled oscillators......Page 121
5.4.1 Coloring two-colomble gmphs......Page 122
5.4.2 Coloring arbitrary graphs......Page 124
5.4.3 Antivoter model for graph colon\'ng......Page 127
5.4.4 Calculating the star chromatic number of a gmph......Page 129
6 Lyapunov Exponents Approach to Synchronization......Page 132
6.1 Continuous-time systems......Page 133
6.2 Discrete-time systems......Page 134
6.3 Three oscillator universal probe for determining synchronization in coupled arrays......Page 135
Appendix A. Some Linear Systems Theory and Matrix Theory......Page 144
Appendix B. Graph Theoretical Definitions and Notations......Page 154
C.1 Lyapunov function and Lyapunov\'s direct or second method......Page 158
C.2 Lyapunov exponents......Page 163
D.1.1 Circuit 1......Page 166
D.1.1 Circuit 2......Page 169
D.2.1 Chua\'s oscillator......Page 170
D.2.2 Piecewise-linear Rossler system......Page 172
D.2.3 Hyperchaotic electronic circuit......Page 173
D.2.4 Hyperchaotic Rossler system......Page 174
Bibliography......Page 178
Index......Page 186