Controlling Chaos (eBook)

Foreword 7
Preface 9
Contents 15
Chapter 1 Overview 20
1.1 The Origin and Development of Chaos Theory 20
1.2 Control of Chaos 22
1.3 Anticontrol of Chaos 29
1.4 Summary 31
References 32
Chapter 2 Preliminaries of Nonlinear Dynamics and Chaos 35
2.1 Introduction 35
2.2 Background 36
2.3 Existence, Uniqueness, Flow, and Dynamical Systems 38
2.4 Equilibrium, Periodic Orbit, Quasiperiodic Orbit, and Poincar´e Map 42
2.5 Invariant and Attracting Sets 47
2.6 Continuous-Time Systems in the Plane 49
2.7 General Solutions of Discrete-Time Linear Systems 55
2.8 Discrete-Time Systems in the Plane 56
2.9 Stabilities of Trajectories I: The Lyapunov First Method 61
2.10 Stabilities of Trajectories II: The Lyapunov Second Method 68
2.11 Chaotic Sets and Chaotic Attractors 71
2.12 Symbolic Dynamics and the Shift Map 72
2.13 Lyapunov Exponent 75
2.14 Examples 77
2.15 Basics of Functional Differential Equations Theory 89
2.16 Summary 93
References 94
Chapter 3 Entrainment and Migration Control of Chaotic Systems 95
3.1 Introduction 95
3.2 Basics on Entrainment and Migration 96
3.3 OPCL Control Scheme 102
3.4 Global Control of a Class of Continuous-Time Polynomial Chaotic Systems 103
3.5 Global Control of a Class of Discrete-Time Systems 113
3.6 Summary 119
References 120
Chapter 4 Feedback Control of Chaotic Systems 121
4.1 Introduction 121
4.2 Model-Reference Adaptive Control of a Class of Discrete-Time Chaotic Systems 122
4.3 Model-Reference Adaptive Control of a Class of Continuous-Time Chaotic Systems 129
4.4 Control of a Class of Chaotic Systems Based on Inverse Optimal Control 143
4.5 Summary 148
References 149
Chapter 5 Synchronizing Chaotic Systems Based on Feedback Control 150
5.1 Introduction 150
5.2 Synchronization of Continuous-Time Chaotic Systems with a Single Input 151
5.3 Synchronization of Multi-Signals in Continuous-Time Chaotic Systems 159
5.4 Synchronization of Different Continuous-Time Chaotic Systems 167
5.5 Synchronization of Discrete-Time Chaotic Systems 174
5.6 Summary 184
References 185
Chapter 6 Synchronizing Chaotic Systems via Impulsive Control 186
6.1 Introduction 186
6.2 Complete Synchronization of a Class of Chaotic Systems via Impulsive Control 187
6.3 Lag-Synchronization of the Unified Systems via Impulsive Control 197
6.4 Impulsive Synchronization of Different Chaotic Systems 204
6.5 Impulsive Synchronization of a Class of Chaotic Delayed Neural Networks 215
6.6 Summary 223
References 223
Chapter 7 Synchronization of Chaotic Systems with Time Delay 225
7.1 Introduction 225
7.2 Adaptive Synchronization of a Class of Delayed Chaotic Systems 226
7.3 Adaptive Synchronization Between Two Different Delayed Chaotic Systems 237
7.4 Synchronization of Chaotic Delayed Neural Networks 254
7.5 Summary 282
References 283
Chapter 8 Synchronizing Chaotic Systems Based on Fuzzy Models 284
8.1 Introduction 284
8.2 Modeling Chaotic Systems via T–S Fuzzy Models 285
8.3 Synchronization of Hyperchaotic Systems via T–S Fuzzy Models 292
8.4 Synchronizing Fuzzy Chaotic Systems with Time-Varying Delays 313
8.5 Summary 321
References 321
Chapter 9 Chaotification of Nonchaotic Systems 323
9.1 Introduction 323
9.2 Chaotification of Discrete-Time Fuzzy Hyperbolic Model with Uncertain Parameters 324
9.3 Chaotification of Continuous-Time Fuzzy Hyperbolic Model Using Impulsive Control 332
9.4 Chaotification of Linear Systems Using Sampled Data Control 341
9.5 Summary 353
References 354
Index 356