Chaos for Engineers Theory, Applications, and Control
Chaos occurs widely in engineering and natural systems. Historically it has been noted only as irregular or unpredictable behaviour and often attributed to random external influences. Further studies have shown that chaotic phenomena are completely deterministic and characteristic for typical nonlin...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1998, 1998
|
| Edition: | 1st ed. 1998 |
| Subjects: | |
| 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
- 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
- 4. Fractals
- 4.1 The Cantor Set
- 4.2 Fractal Dimensions
- 4.3 Fractal Sets
- 4.4 Smale Horseshoe
- 4.5 Fractal Basin Boundaries
- 5. Routes to Chaos
- 5.1 Period Doubling
- 5.2 Quasiperiodic Route
- 5.3 Intermittency
- 5.4 Duffing’s Equation: Discrete Dynamics Approach
- 5.5 Condition for Chaos by Period-Doubling Route
- 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 El Nino Events Model
- 7. Controlling Chaos
- 7.1 Controlling Methods
- 7.2 Synchronization of Chaos
- 7.3 Secure Communication
- References