Measuring Chaos from Spatial Information

Abstract

A new class of Lyapunov exponents are calculated from a simple numerical approach based on a spatially de_ned average of local divergence of trajectories[ This is a new way of identifying chaos in ecological data where\ because of its limited length and quality\ current techniques derived from the dynamical systems theory are not applicable[ In the examples presented\ only a very short time series "around 09 time steps# is necessary for obtaining a close estimate of the spatiotemporal Lyapunov exponent if the lattice size is high enough[ The method is applied to three previously studied coupled map lattice models and is shown to be a good measure for spatiotemporal chaos and an alternative way of estimating the underlying dimension[