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Estimating topological entropy via a symbolic data compression technique.

Yoshito Hirata1, Alistair I Mees

  • 1Centre for Applied Dynamics and Optimization, Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. yoshito@maths.uwa.edu.au

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
Summary

We estimate topological entropy using a parameter-free data compression method. This approach quickly and accurately determines system dynamics from short symbolic sequences.

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Area of Science:

  • Dynamical Systems
  • Information Theory
  • Computational Physics

Background:

  • Topological entropy quantifies complexity in dynamical systems.
  • Estimating topological entropy often requires parameter-heavy symbolic dynamics methods.
  • Existing methods can be sensitive to parameter choices like tree depth.

Purpose of the Study:

  • To introduce a parameter-free method for estimating topological entropy.
  • To leverage data compression techniques for analyzing dynamical systems.
  • To demonstrate the efficiency and accuracy of the context-tree weighting method.

Main Methods:

  • Utilized the context-tree weighting (CTW) method for data compression.
  • Applied CTW to symbolic sequences derived from dynamical systems.

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  • Inferred system transition structure and probabilities automatically.

    • Main Results:

    • The CTW method accurately estimated topological entropy across various systems.
    • Fast convergence was observed, requiring only short symbolic sequences.
    • The method proved to be nearly parameter-free, avoiding ad hoc choices.

    Conclusions:

    • Context-tree weighting offers an efficient and robust approach to estimating topological entropy.
    • This method simplifies the analysis of complex dynamical systems.
    • It provides a powerful alternative to traditional symbolic dynamics techniques.