Boolean Dynamics of Kauffman Models with a Scale-Free Network
| dc.creator | Iguchi, Kazumoto | |
| dc.creator | Kinoshita, Shuichi | |
| dc.creator | Yamada, Hiroaki S. | |
| dc.date | 2005-10-17 | |
| dc.date | 2006-07-28 | |
| dc.date.accessioned | 2026-07-07T06:44:27Z | |
| dc.date.available | 2026-07-07T06:44:27Z | |
| dc.description | 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 ($N \sim 150$), 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 $<k > =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 $<k>$ goes to $<k > =2$. The result supports an existence of the transition at $<k >_c =2$ derived in the annealed model. | |
| dc.description | 10 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0510430 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0510430 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102782 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Boolean Dynamics of Kauffman Models with a Scale-Free Network | |
| dc.type | text |