Chaos for Engineers

Cover
Title page
Prefaces
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 lntroductory 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 Quasi periodic Route
5.3 lntermittency
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
7.1.1 Control Through Feed back
7.1.2 Control by System Design
7.1.3 Selection of Controlling Method
7.2 Synchronisation of Chaos
7.2.1 Pecora and Carroll's Approach
7.2.2 Synchronisation by Continuous Control
7.3 Secure Communication
7.4 Estimation of the Largest Lyapunov Exponent Using Chaos Synchronisation
References
Index