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Related Experiment Videos

Estimating a generating partition from observed time series: symbolic shadowing.

Yoshito Hirata1, Kevin Judd, Devin Kilminster

  • 1Centre for Applied Dynamics and Optimization, School 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
|August 25, 2004
PubMed
Summary

We developed a deterministic algorithm using tessellations to approximate generating partitions from time series data. This method accurately identifies periodic points and estimates metric and topological entropies, even with noisy data.

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Area of Science:

  • Dynamical Systems
  • Time Series Analysis
  • Computational Mathematics

Background:

  • Generating partitions are fundamental for analyzing the dynamics of complex systems.
  • Approximating generating partitions from observed time series data is a challenging problem.
  • Existing methods may struggle with noisy or short datasets.

Purpose of the Study:

  • To propose a novel deterministic algorithm for approximating generating partitions from time series.
  • To evaluate the algorithm's performance using well-known chaotic maps (Hénon and Ikeda).
  • To assess the algorithm's ability to estimate key dynamical invariants like metric and topological entropies.

Main Methods:

  • A deterministic algorithm based on tessellations of the state space is employed.

Related Experiment Videos

  • The algorithm generates partitions from time series data.
  • Performance is validated using time series data from Hénon and Ikeda maps.

    • Main Results:

    • The proposed method successfully produces partitions that uniquely encode periodic points.
    • The algorithm provides accurate estimates of metric and topological entropies.
    • Effective results are obtained even with short and noisy time series data.

    Conclusions:

    • The tessellation-based deterministic algorithm is a viable method for approximating generating partitions.
    • This approach offers a robust tool for analyzing chaotic time series.
    • The method demonstrates utility in estimating essential dynamical properties from limited data.