Permutation complexity of spatiotemporal dynamics

¹  Centro de Investigación Operativa, Universidad Miguel Hernández - 03202 Elche, Spain, EU
²  Departamento de Física, Universidad Rey Juan Carlos - Tulipán s/n 28933 Madrid, Spain, EU

Received: 19 January 2010
Accepted: 23 March 2010

Abstract

We call permutation complexity the kind of dynamical complexity captured by any quantity or functional based on order relations, like ordinal patterns and permutation entropies. These mathematical tools have found interesting applications in time series analysis and abstract dynamical systems. In this letter we propose to extend the study of permutation complexity to spatiotemporal systems, by applying some of its tools to a time series obtained by coarse-graining the dynamics and to state vectors at fixed times, considering the latter as sequences. We show that this approach allows to quantify the complexity and to classify different types of dynamics in cellular automata and in coupled map lattices. Furthermore, we show that our analysis can be used to discriminate between different types of spatiotemporal dynamics registered in magnetoencephalograms.