Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4499232 | Journal of Theoretical Biology | 2007 | 14 Pages |
Abstract
We study the Boolean dynamics of the “quenched” Kauffman models with a directed scale-free network, comparing with that of the original directed random Kauffman networks and that of the directed exponential-fluctuation networks. We have numerically investigated the distributions of the state cycle lengths and its changes as the network size N and the average degree ãkã of nodes increase. In the relatively small network (Nâ¼150), the median, the mean value and the standard deviation grow exponentially with N in the directed scale-free and the directed exponential-fluctuation networks with ãkã=2, where the function forms of the distributions are given as an almost exponential. We have found that for the relatively large Nâ¼103 the growth of the median of the distribution over the attractor lengths asymptotically changes from algebraic type to exponential one as the average degree ãkã goes to ãkã=2. The result supports the existence of the transition at ãkãc=2 derived in the annealed model.
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Authors
Kazumoto Iguchi, Shu-ichi Kinoshita, Hiroaki S. Yamada,