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Robustness of the critical behaviour in a discrete stochastic reaction-diffusion medium

Nazim Fatès 1, * Hugues Berry 2, 3, 4
* Corresponding author
1 MAIA - Autonomous intelligent machine
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 ALCHEMY - Architectures, Languages and Compilers to Harness the End of Moore Years
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
4 COMBINING - COMputational BIology and data miNING
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information, Inria Grenoble - Rhône-Alpes
Abstract : 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.
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Submitted on : Thursday, June 18, 2009 - 11:28:15 AM
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  • HAL Id : inria-00396473, version 1

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Nazim Fatès, Hugues Berry. Robustness of the critical behaviour in a discrete stochastic reaction-diffusion medium. IWNC'09, 2009, Himeji, Japan. ⟨inria-00396473⟩

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