Chaos on a lattice: A systematic investigation of coupled map lattice dynamical systems using statistical metrics

Abstract

This paper contains a large scale systematic survey of coupled map lattice systems, a broad class of dynamical systems. For this study, over 3500 systems were simulated and 11 metrics were computed to describe the behaviour of each system. To the authors’ knowledge, this is the largest-scale study of these types of systems. Four individual investigations were carried out, into the presence of multiple chaotic attractors in systems, the effect of observed dimension choice, the effect of changing the ordering of one-dimensional maps and a large scale survey to identify trends and correlations across systems. The frequency at which systems contain multiple chaotic attractors is estimated to be between 1%–5%. It is also shown that the connectivity of the lattice sites is negatively correlated with the presence of chaos, and also with metrics calculated from the full Lyapunov spectrum, such as the Kaplan–Yorke dimension. The effects of changing the observed dimension is shown to be significant in systems which contain more than one type of one-dimensional map, with substantial variance observed in 50% of systems for some metrics. Map ordering is also found to impact the behaviour of systems in 10%–20% of the systems investigated. The full dataset containing all simulated systems and their computed metrics is made freely available