Finite size stability analysis for stochastic cellular automata

Abstract

Real simulations are performed on a finite size of lattice. It is therefore very difficult to predict a phase diagram on an infinitely large lattice. Here, we present a Finite Size Stability Analysis (FSSA) to know whether the phase is sustainable or not. Although this analysis is a hypothesis, it enables us to determine the boundary of phase diagram. We apply FSSA to multi-state system. For example we study ten-species system in ecology. From computer simulations on various sizes of lattices, we obtain the waiting time τ to extinction. The system is found to have two phases: the coexistence of all species is either unstable or marginally (neutrally) stable. In the latter case, τ diverges on a power law with the increase of lattice size. © 2008 Springer-Verlag Berlin Heidelberg.