PERIODIC AND QUASIPERIODIC TIME-DEPENDENT BEHAVIOR IN COLLECTIVE ORDERED PHASES

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Abstract
We investigate numerically totalistic cellular automata rules in four and five dimensions that have been recently proposed by Chaté and Manneville and that show periodic or quasiperiodic time sequences in the magnetization. We show how to implement such rules fast on a Connection Machine. We confirm the proposed behavior by analyzing the time and size dependence of the distance from the attractor. Also the dependence of the initial configuration, the behavior of very small systems and mean-field calculations are presented.

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