Chaos for Engineers: Theory, Applications, and Control

by Tomasz Kapitaniak

Overview

A desription of the new mathematical ideas in nonlinear dynamics in such a way that engineers can apply them to real physical systems.

Product Details

ISBN-13:	9783540665748
Publisher:	Springer Berlin Heidelberg
Publication date:	04/26/2000
Edition description:	2nd rev. ed. 2000
Pages:	144
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

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.- 7.1.1 Control Through Feedback.- 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.

Editorial Reviews

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."

From the Publisher