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Correlation between Hurst exponent and largest Lyapunov exponent on a coupled map lattice

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  • McAllister, A.
  • McCartney, M.
  • Glass, D.H.

Abstract

Positive correlations have been made between the Hurst exponent and the largest Lyapunov exponent using various one-dimensional maps by other authors. We incorporate these maps into a Coupled Map Lattice (CML), and investigate whether the correlation still exists. With multiple Hurst exponents being calculated for each CML, differences between each have been shown, with the possibility of using one Hurst exponent to represent the system. Results also show that the Hurst exponent is a good indicator of chaos, and is in positive correlation with the largest Lyapunov exponent. We suggest that for a general class of CML, an increased Hurst exponent indicates an increased Lyapunov exponent 85% of the time. Given the Hurst exponent can frequently be calculated more quickly than the Lyapunov exponent we suggest it as a more time efficient measure. Through these connections, machine learning methods have been used to predict the largest Lyapunov exponent for different scenarios.

Suggested Citation

  • McAllister, A. & McCartney, M. & Glass, D.H., 2024. "Correlation between Hurst exponent and largest Lyapunov exponent on a coupled map lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    • Handle: RePEc:eee:phsmap:v:641:y:2024:i:c:s0378437124002346
    DOI: 10.1016/j.physa.2024.129725
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    References listed on IDEAS

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    1. Grech, D & Mazur, Z, 2004. "Can one make any crash prediction in finance using the local Hurst exponent idea?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 133-145.
    2. Tousheng Huang & Huayong Zhang & Xuebing Cong & Ge Pan & Xiumin Zhang & Zhao Liu, 2019. "Exploring Spatiotemporal Complexity of a Predator-Prey System with Migration and Diffusion by a Three-Chain Coupled Map Lattice," Complexity, Hindawi, vol. 2019, pages 1-19, May.
    3. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    4. Tarnopolski, Mariusz, 2018. "Correlation between the Hurst exponent and the maximal Lyapunov exponent: Examining some low-dimensional conservative maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 834-844.
    5. Lotfalinezhad, Hamze & Maleki, Ali, 2020. "TTA, a new approach to estimate Hurst exponent with less estimation error and computational time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    6. Volos, Ch. K. & Kyprianidis, I.M. & Stouboulos, I.N. & Vaidyanathan, S. & Pham, V.-T., 2016. "Analysis, adaptive control and circuit simulation of a novel nonlinear finance systemAuthor-Name: Tacha, O.I," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 200-217.
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