Practical Numerical Algorithms for Chaotic Systems

  • Thomas S. Parker
  • Leon O. Chua

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Thomas S. Parker, Leon O. Chua
    Pages 1-29
  3. Thomas S. Parker, Leon O. Chua
    Pages 31-56
  4. Thomas S. Parker, Leon O. Chua
    Pages 57-82
  5. Thomas S. Parker, Leon O. Chua
    Pages 83-114
  6. Thomas S. Parker, Leon O. Chua
    Pages 115-138
  7. Thomas S. Parker, Leon O. Chua
    Pages 139-166
  8. Thomas S. Parker, Leon O. Chua
    Pages 167-199
  9. Thomas S. Parker, Leon O. Chua
    Pages 201-235
  10. Thomas S. Parker, Leon O. Chua
    Pages 237-267
  11. Thomas S. Parker, Leon O. Chua
    Pages 269-300
  12. Back Matter
    Pages 301-348

About this book

Introduction

One of the basic tenets of science is that deterministic systems are completely predictable-given the initial condition and the equations describing a system, the behavior of the system can be predicted 1 for all time. The discovery of chaotic systems has eliminated this viewpoint. Simply put, a chaotic system is a deterministic system that exhibits random behavior. Though identified as a robust phenomenon only twenty years ago, chaos has almost certainly been encountered by scientists and engi­ neers many times during the last century only to be dismissed as physical noise. Chaos is such a wide-spread phenomenon that it has now been reported in virtually every scientific discipline: astronomy, biology, biophysics, chemistry, engineering, geology, mathematics, medicine, meteorology, plasmas, physics, and even the social sci­ ences. It is no coincidence that during the same two decades in which chaos has grown into an independent field of research, computers have permeated society. It is, in fact, the wide availability of inex­ pensive computing power that has spurred much of the research in chaotic dynamics. The reason is simple: the computer can calculate a solution of a nonlinear system. This is no small feat. Unlike lin­ ear systems, where closed-form solutions can be written in terms of the system's eigenvalues and eigenvectors, few nonlinear systems and virtually no chaotic systems possess closed-form solutions.

Keywords

Nonlinear system algorithms bifurcation stability system

Authors and affiliations

  • Thomas S. Parker
    • 1
  • Leon O. Chua
    • 2
  1. 1.Hewlett PackardSanta RosaUSA
  2. 2.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-3486-9
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8121-4
  • Online ISBN 978-1-4612-3486-9
  • About this book