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Estimating topological entropy using ordinal partition networks.

Konstantinos Sakellariou1,2, Thomas Stemler1, Michael Small1,3

  • 1Complex Systems Group, Department of Mathematics & Statistics, The University of Western Australia, Crawley WA 6009, Australia.

Physical Review. E
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Summary
This summary is machine-generated.

We developed a novel network-based method to approximate topological entropy in chaotic systems. This approach offers more accurate results than existing techniques, even with limited data.

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Area of Science:

  • Dynamical Systems and Chaos Theory
  • Network Science
  • Computational Physics

Background:

  • Topological entropy quantifies chaos in dynamical systems.
  • Existing methods for approximating topological entropy are computationally intensive or less accurate.
  • Ordinal partitions are a key concept in analyzing chaotic dynamics.

Purpose of the Study:

  • To introduce a computationally simple and efficient network-based method for approximating topological entropy.
  • To compare the proposed method with existing ordinal pattern-based techniques.
  • To demonstrate the accuracy and applicability of the new approach.

Main Methods:

  • Constructing a sequence of complex networks based on ordinal partitions.
  • Utilizing the spectral radius of the connectivity matrix for approximation.
  • Applying the method to multidimensional ergodic systems with scalar observables.

Main Results:

  • The network-based method provides significantly more accurate approximations of topological entropy.
  • The logarithm of the spectral radius effectively captures topological entropy.
  • Accuracy is maintained even with low finite values for pattern length.

Conclusions:

  • The proposed network-based method is a computationally efficient and accurate alternative for approximating topological entropy.
  • This approach offers a robust tool for analyzing chaotic systems.
  • The method's reliance on ordinal partitions makes it broadly applicable to various ergodic systems.