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Chaos

From Theory to Applications

  • Anastasios A. Tsonis

Table of contents

  1. Front Matter
    Pages i-xii
  2. Notes

    1. Front Matter
      Pages 1-1
    2. Anastasios A. Tsonis
      Pages 3-5
    3. Anastasios A. Tsonis
      Pages 7-32
    4. Anastasios A. Tsonis
      Pages 33-47
    5. Anastasios A. Tsonis
      Pages 49-63
  3. Theory

    1. Front Matter
      Pages 65-65
    2. Anastasios A. Tsonis
      Pages 67-101
    3. Anastasios A. Tsonis
      Pages 103-136
    4. Anastasios A. Tsonis
      Pages 137-145
  4. Applications

    1. Front Matter
      Pages 147-147
    2. Anastasios A. Tsonis
      Pages 149-187
    3. Anastasios A. Tsonis
      Pages 213-244
  5. Back Matter
    Pages 259-274

About this book

Introduction

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.

Keywords

Mathematica bifurcation chaos dynamical systems dynamics experiment fractal physics

Authors and affiliations

  • Anastasios A. Tsonis
    • 1
  1. 1.University of Wisconsin at MilwaukeeMilwaukeeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-3360-3
  • Copyright Information Springer Science+Business Media New York 1992
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-6482-5
  • Online ISBN 978-1-4615-3360-3
  • Buy this book on publisher's site