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

Jun Hyuk Lee, Il Seung Park and Jooeun Ahn

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

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.

Keywords: Dynamical system; Maximal Lyapunov exponent; State space reconstruction; Principal component analysis; Noise-robustness (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923008172

DOI: 10.1016/j.chaos.2023.113916

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