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Journal Articles International Journal of Unconventional Computing Year : 2011

Robustness of the Critical Behaviour in the Stochastic Greenberg-Hastings Cellular Automaton Model

Abstract

We study a stochastic version of the Greenberg-Hastings cellular automa- ton, a simple model of wave propagation in reaction-diffusion media. Despite its apparent simplicity, its global dynamics displays various com- plex behaviours. Here, we investigate the influence of temporary or definitive failures of the cells of the grid. We show that a continuous decrease of the probability of excitation of cells triggers a drastic change of behaviour, driving the system from an "active" to an "extinct" steady state. Simulations show that this phenomenon is a nonequilibrium phase transition that belongs to directed percolation universality class. Obser- vations show an amazing robustness of the critical behaviour with regard to topological perturbations: not only is the phase transition occurrence preserved, but its universality class remains directed percolation. We also demonstrate that the position of the critical threshold can be easily pre- dicted as it decreases linearly with the inverse of the average number of neighbours per cell.
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Dates and versions

inria-00598379 , version 1 (06-06-2011)

Identifiers

  • HAL Id : inria-00598379 , version 1

Cite

Hugues Berry, Nazim Fatès. Robustness of the Critical Behaviour in the Stochastic Greenberg-Hastings Cellular Automaton Model. International Journal of Unconventional Computing, 2011, 7 (1-2), pp.65-85. ⟨inria-00598379⟩
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