Correlation between the Hurst exponent and the maximal Lyapunov exponent: Examining some low-dimensional conservative maps

Mariusz Tarnopolski

Physica A: Statistical Mechanics and its Applications, 2018, vol. 490, issue C, 834-844

Abstract: The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this space. A tight correlation between the HEs and mLEs is found, with the Spearman rank ρ=0.83 and ρ=0.75 for the Chirikov and 2D Froeschlé maps, respectively. Based on this relation, a machine learning (ML) procedure, using the nearest neighbor algorithm, is performed to reproduce the HE distribution based on the mLE distribution alone. A few thousand HE and mLE values from the mixed spaces were used for training, and then using 2−2.4×105 mLEs, the HEs were retrieved. The ML procedure allowed to reproduce the structure of the mixed spaces in great detail.

Keywords: Conservative systems; Chirikov standard map; Maximal Lyapunov exponent; Hurst exponent; Machine learning (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:490:y:2018:i:c:p:834-844

DOI: 10.1016/j.physa.2017.08.159

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