Chaos for Engineers Theory, Applications, and Control
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 c...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2000, 2000
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| Edition: | 2nd ed. 2000 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Response of a Nonlinear System
- Problems
- 2. Continuous Dynamical Systems
- 2.1 Phase Space and Attractors
- 2.2 Fixed Points and Linearisation
- 2.3 Relation Between Nonlinear and Linear Systems
- 2.4 Poincaré Map
- 2.5 Lyapunov Exponents and Chaos
- 2.6 Spectral Analysis
- 2.7 Description of Different Attractors
- 2.8 Reconstruction of Attractor from Time Series
- Problems
- 3. Discrete Dynamical Systems
- 3.1 Introductory Example
- 3.2 One-Dimensional Maps
- 3.3 Bifurcations of One-Dimensional Maps
- 3.4 One-Dimensional Maps and Higher-Dimensional Systems
- Problems
- 4. Fractals
- 4.1 The Cantor Set
- 4.2 Fractal Dimensions
- 4.3 Fractal Sets
- 4.4 Smale Horseshoe
- 4.5 Fractal Basin Boundaries
- Problems
- 5. Routes to Chaos
- 5.1 Period-Doubling
- 5.2 Quasiperiodic Route
- 5.3 Intermittency
- 5.4 Duffing’s Oscillator: Discrete Dynamics Approach
- 5.5 Condition for Chaos by Period Doubling Route
- Problems
- 6. Applications
- 6.1 Chaos in Systems with Dry Friction
- 6.2 Chaos in Chemical Reactions
- 6.3 Elastica and Spatial Chaos
- 6.4 Electronic Circuits and Chaos
- 6.5 Chaos in Model of El Nino Events
- 7. Controlling Chaos
- 7.1 Controlling Methods
- 7.2 Synchronisation of Chaos
- 7.3 Secure Communication
- 7.4 Estimation of the Largest Lyapunov Exponent Using Chaos Synchronisation
- References