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- W2950851825 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 $ $ of nodes increase. In the relatively small network ($N sim 150$), 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 $ =2 $, where the function forms of the distributions are given as an almost exponential. We have found that for the relatively large $N sim 10^3$ the growth of the median of the distribution over the attractor lengths asymptotically changes from algebraic type to exponential one as the average degree $ $ goes to $ =2$. The result supports an existence of the transition at $ _c =2$ derived in the annealed model." @default.
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- W2950851825 date "2005-10-17" @default.
- W2950851825 modified "2023-09-27" @default.
- W2950851825 title "Boolean Dynamics of Kauffman Models with a Scale-Free Network" @default.
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