ISBN: 3-540-66574-9
TITLE: Chaos for Engineers
AUTHOR: Kapitaniak, Tomasz
TOC:

1. Response of a Nonlinear System 1
Problems 4
2. Continuous Dynamical Systems 5
2.1 Phase Space and Attractors 5
2.2 Fixed Points and Linearisation 11
2.3 Relation Between Nonlinear and Linear Systems 17
2.4 Poincar Map 20
2.5 Lyapunov Exponents and Chaos 23
2.6 Spectral Analysis 27
2.7 Description of Different Attractors 31
2.8 Reconstruction of Attractor from Time Series 31
Problems 35
3. Discrete Dynamical Systems 39
3.1 Introductory Example 39
3.2 One-Dimensional Maps 40
3.3 Bifurcations of One-Dimensional Maps 48
3.4 One-Dimensional Maps and Higher-Dimensional Systems 49
Problems 52
4. Fractals 53
4.1 The Cantor Set 53
4.2 Fractal Dimensions 56
4.3 Fractal Sets 59
4.4 Smale Horseshoe 61
4.5 Fractal Basin Boundaries 64
Problems 67
5. Routes to Chaos 69
5.1 Period-Doubling 69
5.2 Quasiperiodic Route 71
5.3 Intermittency 74
5.4 Duffing's Oscillator: Discrete Dynamics Approach 77
5.5 Condition for Chaos by Period Doubling Route 80
Problems 85
6. Applications 87
6.1 Chaos in Systems with Dry Friction. 87
6.2 Chaos in Chemical Reactions 94
6.3 Elastica and Spatial Chaos 97
6.4 Electronic Circuits and Chaos 99
6.5 Chaos in Model of El Nino Events 105
7. Controlling Chaos 111
7.1 Controlling Methods 111
7.1.1 Control Through Feedback 111
7.1.2 Control by System Design 115
7.1.3 Selection of Controlling Method 119
7.2 Synchronisation of Chaos 120
7.2.1 Pecora and Carroll's Approach 120
7.2.2 Synchronisation by Continuous Control 122
7.3 Secure Communication 127
7.4 Estimation of the Largest Lyapunov Exponent Using Chaos Synchronisation 131
References 137
Index 141
END
