Chaos for Engineers: Theory, Applications, and Control

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Springer Science & Business Media, Mar 15, 2000 - Computers - 142 pages
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Chaos occurs widely in both natural and man-made systems. Recently, examples of the potential usefulness of chaotic behavior have caused growing interest among engineers and applied scientists. In this book the new mathematical ideas in nonlinear dynamics are described in such a way that engineers can apply them to real physical systems. From a review of the first edition by Prof. El Naschie, University of Cambridge: "Small is beautiful and not only that, it is comprehensive as well. These are the spontaneous thoughts which came to my mind after browsing in this latest book by Prof. Thomas Kapitaniak, probably one of the most outstanding scientists working on engineering applications of Nonlinear Dynamics and Chaos today. A more careful reading reinforced this first impression....The presentation is lucid and user friendly with theory, examples, and exercises.... I thought that one can no longer write text books in nonlinear dynamics which could have important impact of fill a gap. Tomasz Kapitaniak's newest book has proved me wrong twofold."
 

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Contents

1 Response of a Nonlinear System
1
Problems
4
2 Continuous Dynamical Systems
5
22 Fixed Points and Linearisation
11
23 Relation Between Nonlinear and Linear Systems
17
24 Poincare Map
20
25 Lyapunov Exponents and Chaos
23
26 Spectral Analysis
27
5 Routes to Chaos
69
52 Quasiperiodic Route
71
53 Intermittency
74
Discrete Dynamics Approach
77
55 Condition for Chaos by Period Doubling Route
80
Problems
85
6 Applications
87
62 Chaos in Chemical Reactions
94

27 Description of Different Attractors
31
Problems
35
3 Discrete Dynamical Systems
39
32 OneDimensional Maps
40
33 Bifurcations of OneDimensional Maps
48
34 OneDimensional Maps and HigherDimensional Systems
49
Problems
52
4 Fractals
53
42 Fractal Dimensions
56
43 Fractal Sets
59
44 Smale Horseshoe
61
45 Fractal Basin Boundaries
64
Problems
67
63 Elastica and Spatial Chaos
97
64 Electronic Circuits and Chaos
99
65 Chaos in Model of El Nino Events
105
7 Controlling Chaos
111
712 Control by System Design
115
713 Selection of Controlling Method
119
72 Synchronisation of Chaos
120
722 Synchronisation by Continuous Control
122
73 Secure Communication
127
74 Estimation of the Largest Lyapunov Exponent Using Chaos Synchronisation
131
References
137
Index
141
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About the author (2000)

Kapitaniak-Technical University of Lodz