Measuring Chaos from Spatial Information

Abstract A new class of Lyapunov exponents are calculated from a simple numerical approach based on a spatially defined 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 10 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.