Directed percolation in a two-dimensional stochastic fire-diffuse-fire model

We establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release that retains both the discrete nature of calcium stores and the stochastic nature of release. It is formed from an array of noisy threshold elements that are coupled only by a diffusing signal. The model supports spontaneous release events that can merge to form spreading circular and spiral waves of activity. The critical level of noise required for the system to exhibit a nonequilibrium phase transition between propagating and nonpropagating waves is obtained by an examination of the local slope delta (t) of the survival probability Pi(t) proportional exp [-delta(t)] for a wave to propagate for a time t .