Simple estimation method for the largest Lyapunov exponent of continuous fractional-order differential equations

In this paper, a simple method based on the perturbation of the initial value is presented to directly estimate the largest Lyapunov exponent (LLE) from continuous fractional-order differential equations. Two nearby trajectories are used to directly compute the LLE and reduce parameter errors. Another initial value is obtained by perturbing the given initial value. Two solutions are then developed from a fractional-order chaotic system by using the two initial values. The evolutionary distance between the two solutions is calculated, and the LLE is determined from the curve of the track distance. Some continuous fractional-order chaotic and nonchaotic differential equations are applied to verify the effectiveness of our method. Experimental results indicate that the proposed method is feasible and easy to implement instead of computing the Jacobian matrix and phase space. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a simple method based on perturbing the initial value to directly estimate the largest Lyapunov exponent. The method reduces parameter errors and is feasible and easy to implement without computing the Jacobian matrix and phase space.