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

Timofeeva, Yulia and Coombes, Stephen (2004) Directed percolation in a two dimensional stochastic fire-diffuse-fire model.

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## Abstract

In this paper 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 the 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 non-equilibrium phase-transition between propagating and non-propagating waves is obtained by an examination of the \textit{local slope} $\delta(t)$ of the survival probability, $\Pi(t) \propto \exp(- \delta(t))$, for a wave to propagate for a time $t$.

Item Type: Article To appear in Physical Review E directed percolation, calcium, fire-diffuse-fire Faculty of Science > School of Mathematical Sciences 134 Coombes, Prof Stephen 19 Oct 2004 27 Jun 2011 11:24

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