Critical phenomena in a discrete stochastic reaction-diffusion medium

We study the steady states of a reaction-diffusion medium modelled by a stochastic 2D cellular automaton. We consider the Greenberg-Hastings model where noise and topological irregularities of the grid are taken into account. The decrease of the probability of excitation changes qualitatively the behaviour of the system from an “active” to an “extinct” steady state. Simulations show that this change occurs near a critical threshold ; it is identified as a nonequilibrium phase transition which belongs to the directed percolation universality class. We test the robustness of the phenomenon by introducing persistent defects in the topology : directed percolation behaviour is conserved. Using experimental and analytical tools, we suggest that the critical threshold varies as the inverse of the average number of neighbours per cell. keywords: reaction-diffusion media, stochastic cellular automata, phase transitions Foreword: See http://webloria.loria.fr/fates/Amybia/reacdiff.html for accessing the complete set of experiments this paper refers to. The simulations presented in this paper were made with the FiatLux [Fat] cellular automata simulator.