Computing Lyapunov exponents based on the solution expression of the variational system

Abstract

A simple discrete QR algorithm based on a solution expression of the variational equation of a dynamical system is presented for computing the Lyapunov exponents of n-dimensional continuous dynamical systems. The developed numerical scheme of study is based on a time integration using a constant time-step fourth-order Adams–Bashforth method. Numerical results are presented for a Lorenz system with known Lyapunov exponents, and higher dimensional dynamical systems. The algorithm proposed to compute the Lyapunov exponents is found to be robust, computationally efficient, and stable for a sufficiently small step-size h.