書誌事項

Nonlinear time series analysis

Holger Kantz, Thomas Schreiber

(Cambridge nonlinear science series, 7)

Cambridge University Press, 1997

  • : hbk
  • : pbk

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注記

Includes bibliographical references (p. 288-299) and index

内容説明・目次

内容説明

Deterministic chaos provides a novel framework for the analysis of irregular time series. Traditionally, nonperiodic signals are modeled by linear stochastic processes. But even very simple chaotic dynamical systems can exhibit strongly irregular time evolution without random inputs. Chaos theory offers completely new concepts and algorithms for time series analysis which can lead to a thorough understanding of the signal. The book introduces a broad choice of such concepts and methods, including phase space embeddings, nonlinear prediction and noise reduction, Lyapunov exponents, dimensions and entropies, as well as statistical tests for nonlinearity. Related topics like chaos control, wavelet analysis and pattern dynamics are also discussed. Applications range from high quality, strictly deterministic laboratory data to short, noisy sequences which typically occur in medicine, biology, geophysics or the social sciences. All material is discussed and illustrated using real experimental data.

目次

  • Part I. Basic Concepts: 1. Introduction: why nonlinear methods?
  • 2. Linear tools and general considerations
  • 3. Phase space methods
  • 4. Determinism and predictability
  • 5. Instability: Lyapunov exponents
  • 6. Self-similarity: dimensions
  • 7. Using nonlinear methods when determinism is weak
  • 8. Selected nonlinear phenomena
  • Part II. Advanced Topics: 9. Advanced embedding methods
  • 10. Chaotic data and noise
  • 11. More about invariant quantities
  • 12. Modeling and forecasting
  • 13. Chaos control
  • 14. Other selected topics
  • Appendix 1. Efficient neighbour searching
  • Appendix 2. Program listings
  • Appendix 3. Description of the experimental data sets.

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