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

Timofeeva, Yulia; Coombes, Stephen

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 $t$.

Citation

Timofeeva, Y., & Coombes, S. (2004). Directed percolation in a two dimensional stochastic fire-diffuse-fire model

• Journal Article Type: Article
• Publication Date: Sep 1, 2004
• Deposit Date: Oct 19, 2004
• Publicly Available Date: Oct 9, 2007
• Peer Reviewed: Peer Reviewed
• Keywords: directed percolation, calcium, fire-diffuse-fire
• Public URL: https://nottingham-repository.worktribe.com/output/1020914
• Additional Information: To appear in Physical Review E