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Chaos

From Theory to Applications

  • Book
  • © 1992

Overview

Authors:
  1. Anastasios A. Tsonis

    1. University of Wisconsin at Milwaukee, Milwaukee, USA

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xii
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  2. Notes

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Anastasios A. Tsonis
      Pages 3-5

    3. Mathematical Notes

      • Anastasios A. Tsonis
      Pages 7-32

    4. Physics Notes

      • Anastasios A. Tsonis
      Pages 33-47

    5. On Fractals

      • Anastasios A. Tsonis
      Pages 49-63

  3. Theory

    1. Front Matter

      Pages 65-65
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    2. Attractors

      • Anastasios A. Tsonis
      Pages 67-101

    3. Bifurcations and Routes to Chaos

      • Anastasios A. Tsonis
      Pages 103-136

    4. Chaos Elsewhere

      • Anastasios A. Tsonis
      Pages 137-145

  4. Applications

    1. Front Matter

      Pages 147-147
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    2. Reconstruction of Dynamics from Observables

      • Anastasios A. Tsonis
      Pages 149-187

    3. Evidence of Chaos in “Controlled” and “Uncontrolled” Experiments

      • Anastasios A. Tsonis
      Pages 189-212

    4. Nonlinear Time Series Forecasting

      • Anastasios A. Tsonis
      Pages 213-244

    5. Other Developments and Trends in the Application of Chaos

      • Anastasios A. Tsonis
      Pages 245-258

  5. Back Matter

    Pages 259-274
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Keywords

About this book

Based on chaos theory two very important points are clear: (I) random­ looking aperiodic behavior may be the product of determinism, and (2) nonlinear problems should be treated as nonlinear problems and not as simplified linear problems. The theoretical aspects ofchaos have been presented in great detail in several excellent books published in the last five years or so. However, while the problems associated with applications of the theory-such as dimension and Lyapunov exponentsestimation, chaosand nonlinear pre­ diction, and noise reduction-have been discussed in workshops and ar­ ticles, they have not been presented in book form. This book has been prepared to fill this gap between theory and ap­ plicationsand to assist studentsand scientists wishingto apply ideas from the theory ofnonlinear dynamical systems to problems from their areas of interest. The book is intended to be used as a text for an upper-level undergraduate or graduate-level course, as well as a reference source for researchers. My philosophy behind writing this book was to keep it simple and informative without compromising accuracy. I have made an effort to presentthe conceptsby usingsimplesystemsand step-by-stepderivations. Anyone with an understanding ofbasic differential equations and matrix theory should follow the text without difficulty. The book was designed to be self-contained. When applicable, examples accompany the theory. The reader will notice, however, that in the later chapters specific examples become less frequent. This is purposely done in the hope that individuals will draw on their own ideas and research projects for examples.

Authors and Affiliations

  • University of Wisconsin at Milwaukee, Milwaukee, USA

    Anastasios A. Tsonis

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