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Analysis of Observed Chaotic Data

  • Textbook
  • © 1996

Overview

Authors:
  1. Henry D. I. Abarbanel

    1. Institute for Nonlinear Science, University of California—San Diego, La Jolla, USA

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  • Bestselling title now available as inexpensive softcover * * Provides a toolkit of tried-and-tested methods for analyzing signals from nonlinear sources * Methods are applicable in physics, biology, geophysics, and control and communications engineering *
  • Many illustrative examples

Part of the book series: Institute for Nonlinear Science (INLS)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • Henry D. I. Abarbanel
    Pages 1-12

  3. Reconstruction of Phase Space

    • Henry D. I. Abarbanel
    Pages 13-23

  4. Choosing Time Delays

    • Henry D. I. Abarbanel
    Pages 25-37

  5. Choosing the Dimension of Reconstructed Phase Space

    • Henry D. I. Abarbanel
    Pages 39-67

  6. Invariants of the Motion

    • Henry D. I. Abarbanel
    Pages 69-93

  7. Modeling Chaos

    • Henry D. I. Abarbanel
    Pages 95-114

  8. Signal Separation

    • Henry D. I. Abarbanel
    Pages 115-132

  9. Control and Chaos

    • Henry D. I. Abarbanel
    Pages 133-145

  10. Synchronization of Chaotic Systems

    • Henry D. I. Abarbanel
    Pages 147-172

  11. Other Example Systems

    • Henry D. I. Abarbanel
    Pages 173-215

  12. Estimating in Chaos: Cramér-Rao Bounds

    • Henry D. I. Abarbanel
    Pages 217-235

  13. Summary and Conclusions

    • Henry D. I. Abarbanel
    Pages 237-247

  14. Back Matter

    Pages 249-272
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Keywords

About this book

When I encountered the idea of chaotic behavior in deterministic dynami­ cal systems, it gave me both great pause and great relief. The origin of the great relief was work I had done earlier on renormalization group properties of homogeneous, isotropic fluid turbulence. At the time I worked on that, it was customary to ascribe the apparently stochastic nature of turbulent flows to some kind of stochastic driving of the fluid at large scales. It was simply not imagined that with purely deterministic driving the fluid could be turbulent from its own chaotic motion. I recall a colleague remarking that there was something fundamentally unsettling about requiring a fluid to be driven stochastically to have even the semblance of complex motion in the velocity and pressure fields. I certainly agreed with him, but neither of us were able to provide any other reasonable suggestion for the observed, apparently stochastic motions of the turbulent fluid. So it was with relief that chaos in nonlinear systems, namely, complex evolution, indistinguish­ able from stochastic motions using standard tools such as Fourier analysis, appeared in my bag of physics notions. It enabled me to have a physi­ cally reasonable conceptual framework in which to expect deterministic, yet stochastic looking, motions. The great pause came from not knowing what to make of chaos in non­ linear systems.

Authors and Affiliations

  • Institute for Nonlinear Science, University of California—San Diego, La Jolla, USA

    Henry D. I. Abarbanel

Bibliographic Information

  • Book Title: Analysis of Observed Chaotic Data

  • Authors: Henry D. I. Abarbanel

  • Series Title: Institute for Nonlinear Science

  • DOI: https://doi.org/10.1007/978-1-4612-0763-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1996

  • Hardcover ISBN: 978-0-387-94523-1Published: 29 November 1995

  • Softcover ISBN: 978-0-387-98372-1Published: 07 November 1997

  • eBook ISBN: 978-1-4612-0763-4Published: 06 December 2012

  • Series ISSN: 1431-4673

  • Edition Number: 1

  • Number of Pages: XIV, 272

  • Topics: Physics, general

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