Chaos for Engineers: Theory, Applications, and Control

ISBN-13: 9783540665748 / Angielski / Miękka / 2000 / 144 str.

Tomasz Kapitaniak; T. Kapitaniak

Opis

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."

Recenzje

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."

Spis treści

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.

Blurb

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."