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Divergence measure between chaotic attractors.

L Diambra1

  • 1Departamento de Fisiologia e Biofísica, Universidade de São Paulo, Avenue Professor Lineu Prestes 1524, ICB1 CEP 05508-900, São Paulo, SP Brazil. diambria@fisio.icb.usp.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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We developed a new method using generalized entropy to measure how different two chaotic attractors are. This technique can also detect changes in time series data.

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Information Theory
  • Time Series Analysis

Background:

  • Quantifying the dissimilarity between complex systems is crucial.
  • Chaotic attractors represent the long-term behavior of dynamical systems.
  • Existing methods may not adequately capture subtle differences.

Purpose of the Study:

  • To introduce a novel measure for quantifying the dissimilarity of probability distributions.
  • To apply this measure to assess the divergence of chaotic attractors.
  • To demonstrate its utility in detecting nonstationary events in time series.

Main Methods:

  • Definition of a divergence measure based on generalized entropy.
  • Application to the Hénon attractor under additive noise.

Related Experiment Videos

  • Analysis of time series data for event detection.

    • Main Results:

    • The proposed measure effectively quantifies the dissimilarity between chaotic attractors.
    • The method successfully illustrates the impact of noise on attractor divergence.
    • Nonstationary events in time series can be reliably detected.

    Conclusions:

    • The generalized entropy-based divergence measure offers a robust tool for analyzing chaotic systems.
    • This approach provides insights into the effects of perturbations like noise.
    • The method has practical applications in time series analysis and event detection.