Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
1993-04-26
Nonlinear Sciences
Adaptation and Self-Organizing Systems
12 pages. A uuencoded, tar-compressed postscipt file containing figures has been added
Scientific paper
10.1016/0167-2789(93)90190-C
A variant of Kauffman's model of cellular metabolism is presented. It is a randomly generated network of boolean gates, identical to Kauffman's except for a small bias in favor of boolean gates that depend on at most one input. The bias is asymptotic to 0 as the number of gates increases. Upper bounds on the time until the network reaches a state cycle and the size of the state cycle, as functions of the number of gates $n$, are derived. If the bias approaches 0 slowly enough, the state cycles will be smaller than $n^c$ for some $c<1$. This lends support to Kauffman's claim that in his version of random network the average size of the state cycles is approximately $n^{1/2}$.
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