Relaxation and limit cycles in a global version of the quenched Kauffman model

Krzysztof Kułakowski

Physica A: Statistical Mechanics and its Applications, 1995, vol. 216, issue 1, 120-127

Abstract: A combinatorial method is used to investigate all possible cellular automata, defined on a finite set of w global configurations. Relaxation time is defined as the number of steps before entering a fixed point or a cycle. For given w, we derive an analytical formula for the distribution of relaxation times t: Pw(t) = (w!/ww + 1)Σk = 0w−t−1(wk/k!). The same distribution is proved to be valid for the length of limit cycles. The results have some relevance to the quenched Kauffman model.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:216:y:1995:i:1:p:120-127

DOI: 10.1016/0378-4371(95)00017-2

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