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Practical Numerical Algorithms for Chaotic Systems

  • Book
  • © 1989

Overview

Authors:
  1. Thomas S. Parker

    1. Hewlett Packard, Santa Rosa, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Leon O. Chua

    1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Steady-State Solutions and Limit Sets

    • Thomas S. Parker, Leon O. Chua
    Pages 1-29

  3. Poincaré Maps

    • Thomas S. Parker, Leon O. Chua
    Pages 31-56

  4. Stability of Limit Sets

    • Thomas S. Parker, Leon O. Chua
    Pages 57-82

  5. Integration of Trajectories

    • Thomas S. Parker, Leon O. Chua
    Pages 83-114

  6. Locating Limit Sets

    • Thomas S. Parker, Leon O. Chua
    Pages 115-138

  7. Stable and Unstable Manifolds

    • Thomas S. Parker, Leon O. Chua
    Pages 139-166

  8. Dimension

    • Thomas S. Parker, Leon O. Chua
    Pages 167-199

  9. Bifurcation Diagrams

    • Thomas S. Parker, Leon O. Chua
    Pages 201-235

  10. Programming

    • Thomas S. Parker, Leon O. Chua
    Pages 237-267

  11. Phase Portraits

    • Thomas S. Parker, Leon O. Chua
    Pages 269-300

  12. Back Matter

    Pages 301-348
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Keywords

About this book

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.

Authors and Affiliations

  • Hewlett Packard, Santa Rosa, USA

    Thomas S. Parker

  • Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA

    Leon O. Chua

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