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

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.