We study a stochastic version of the Greenberg-Hastings cellular#R##N#automaton, a simple model of wave propagation in reactiondiffusion#R##N#media. Despite its apparent simplicity, its global dynamics#R##N#frequently show complex behaviours. Here, we investigate#R##N#the influence of temporary or definitive failures of the cells#R##N#of the grid. We show that a continuous decrease of the probability#R##N#of excitation of cells triggers a drastic change of behaviour, driving#R##N#the system from an “active” to an “extinct” steady state. Simulations#R##N#show that this phenomenon is a sharp transition which#R##N#is a nonequilibrium phase transition. We identify its universality#R##N#class as directed percolation and we examine how it is affected#R##N#by various changes in the topology. The results show an amazing#R##N#robustness of the critical behavior with regard to such topological#R##N#perturbations: not only is the phase transition occurrence#R##N#preserved, but its universality class remains directed percolation.#R##N#We also show that the position of the critical threshold can be#R##N#easily predicted as it decreases linearly with the inverse of the#R##N#average number of neighbours per cell.
['Hugues Berry', 'Nazim Fatès']
Robustness of the Critical Behaviour in the Stochastic Greenberg-Hastings Cellular Automaton Model ∗