CRITICAL BEHAVIOR OF A PROBABILISTIC LOCAL AND NONLOCAL SITE-EXCHANGE CELLULAR AUTOMATON

N. Boccara, J. Nasser and M. Roger
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N. Boccara: DRECAM-SPEC, CE Saclay, 91191 Gif-sur-Yvette Cedex, France
J. Nasser: DRECAM-SPEC, CE Saclay, 91191 Gif-sur-Yvette Cedex, France
M. Roger: DRECAM-SPEC, CE Saclay, 91191 Gif-sur-Yvette Cedex, France

International Journal of Modern Physics C (IJMPC), 1994, vol. 05, issue 03, 537-545

Abstract: We study the critical behavior of a probabilistic automata network whose local rule consists of two subrules. The first one, applied synchronously, is a probabilistic one-dimensional range-one cellular automaton rule. The second, applied sequentially, exchanges the values of a pair of sites. According to whether the two sites are first-neighbors or not, the exchange is said to be local or nonlocal. The evolution of the system depends upon two parameters, the probability p characterizing the probabilistic cellular automaton, and the degree of mixing m resulting from the exchange process. Depending upon the values of these parameters, the system exhibits a bifurcation similar to a second order phase transition characterized by a nonnegative order parameter, whose role is played by the stationary density of occupied sites. When m is very large, the correlations created by the application of the probabilistic cellular automaton rule are destroyed, and, as expected, the behavior of the system is then correctly predicted by a mean-field-type approximation. According to whether the exchange of the site values is local or nonlocal, the critical behavior is qualitatively different as m varies.

Keywords: Cellular Automata; Critical Behavior (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1142/S0129183194000714

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