High precision numerical estimation of the largest Lyapunov exponent

Abstract

A numerical algorithm for estimating the largest Lyapunov exponent of a chaotic attractor is presented. The method makes use of the minimal time for two trajectories to diverge beyond a given distance from each other. We define the nth divergence speed G(n) and show that, for an appropriate range of n, the largest Lyapunov exponent can be approximated by G(n). (C) 2009 Elsevier B.V. All rights reserved.