Cellular automata with inertia: Species competition, spatial patterns, and survival in ecotones

Abstract

We consider a two-dimensional CA model with three possible states for the system individual cells, 0 and . As for the dynamical rules, only can exert pressure to change the cells actual states. In this way, the 0 state is neutral and in some sense competitively weaker than the other two states. We further assume an inner property, the inertia, which is an intrinsic resistance to changes in the system. We evolve an ensemble of initial configurations for the CA until reaching steady states. By calculating averages over some relevant quantities for the final stationary configurations, we discuss how certain features of the problem, namely, initial states population and degree of aggregation as well as the values of inertia, can determine the different characteristics of the spatio-temporal pattern created by the CA evolution. We finally discuss how our findings may be relevant in the understanding of structures formation due to species competition in biology, specially in the transition regions between different biomes, the so called ecotones. © 2010 IOP Publishing Ltd.