2005/10/17 by Kazumoto Iguchi, Shuichi Kinoshita, Iguchi, Kazumoto +4
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Gene Regulatory Network Analysis #Protein Structure and Dynamics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0510430
10 pages, 8 figures
openalex publication_date 2005/10/17 · arxiv created 2006/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 <k> of nodes increase. In the relatively small network (N ∼ 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 <k > =2 , where the function forms of the distributions are given as an almost exponential. We have found that for the relatively large N ∼ 103 the growth of the median of the distribution over the attractor lengths asymptotically changes from algebraic type to exponential one as the average degree <k> goes to <k > =2. The result supports an existence of the transition at <k >c =2 derived in the annealed model.