Implementation of approach to compute the Lyapunov characteristic exponents for continuous dynamical systems to higher dimensions

Abstract

A general method for accurately computing the Lyapunov characteristic exponents (LCEs) of continuous dynamical systems has been developed in [10]. In this paper, this method is extended to implementations on systems of arbitrary dimensions. An accurate implementation of the extension of the method to compute LCEs that uses available numerical techniques is presented for systems of arbitrary dimensions. Previously in [10], the original approach had only been implemented for general systems of up to dimension three. Closed form expressions for the exponential of skew symmetric matrices of order 4 and 5 will be presented. These formulas are used to obtain an accurate and efficient implementation of the method for dynamical systems of dimensions 4 and 5. Numerical examples illustrating the accuracy of the implementations are presented.