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

Hugues Berry 1, 2, 3 Nazim Fatès 4
2 BEAGLE - Artificial Evolution and Computational Biology
LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558, Inria Grenoble - Rhône-Alpes, LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
3 COMBINING - COMputational BIology and data miNING
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information, Inria Grenoble - Rhône-Alpes
4 MAIA - Autonomous intelligent machine
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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.
Document type :
Journal articles
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https://hal.inria.fr/inria-00598379
Contributor : Nazim Fatès <>
Submitted on : Monday, June 6, 2011 - 2:03:12 PM
Last modification on : Monday, February 10, 2020 - 4:36:52 PM

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  • HAL Id : inria-00598379, version 1

Citation

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

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