A Jacobian approach for calculating the Lyapunov exponents of short time series using support vector regression

Abstract

In order to characterize a system and to analyze the predictability of the time series under investigation, the detection of chaos and fractal behavior in experimental data is essential. In this work, support vector regression with two different kernel types namely, the linear kernel and sigmoid kernel, has been utilized for the calculation of the Lyapunov exponents of the given time series. The developed technique for the estimation of Lyapunov exponents has been validated with the help of time series generated from well known chaotic maps and also by comparing the Lyapunov exponents obtained using Rosenstein method. The results of this work reveal that the proposed technique is capable of producing accurate positive exponents for all the considered chaotic maps.