The computation of Lyapunov exponents via spatial integration with application to blowout bifurcations

摘要

We propose a new method for the numerical approximation of the largest Lyapunov exponent. This method is based on the computation of a spatial average with respect to an underlying (natural) invariant measure rather than on a long-term simulation of the dynamical system. This approach is particularly advantageous for the detection of blowout bifurcations of a synchronous chaotic state, and we illustrate this fact for a system of two coupled Duffing oscillators.