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Noise-robust estimation of the maximal Lyapunov exponent based on state space reconstruction with principal components

Author

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  • Lee, Jun Hyuk
  • Park, Il Seung
  • Ahn, Jooeun

Abstract

The maximal Lyapunov exponent (MLE) is a widely used indicator of the dependence on initial conditions of various systems in many fields. However, both the accuracy and the consistency of the conventional method for estimating MLE heavily depend on the noise level. We developed a method for estimating MLE with higher accuracy and noise-robustness compared with the conventional method. Considering that state space reconstruction using principal components can enhance noise-robustness when appropriate parameter values are used, we devised a set of algorithms for finding proper window length and the number of principal components required for state space reconstruction and MLE estimation. Numerical simulations of multiple dynamical systems with various data lengths and noise levels verified that the devised algorithm yields more accurate, consistent, and noise-robust estimation of MLE than the conventional method.

Suggested Citation

  • Lee, Jun Hyuk & Park, Il Seung & Ahn, Jooeun, 2023. "Noise-robust estimation of the maximal Lyapunov exponent based on state space reconstruction with principal components," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923008172
    DOI: 10.1016/j.chaos.2023.113916
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    References listed on IDEAS

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    1. Dominique Guégan, 2007. "Chaos in economics and finance," Documents de travail du Centre d'Economie de la Sorbonne b07054, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2009.
    2. Alexey N. Pavlov & Olga N. Pavlova & Jürgen Kurths, 2017. "Determining the largest Lyapunov exponent of chaotic dynamics from sequences of interspike intervals contaminated by noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(4), pages 1-8, April.
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