Iguchi Kazumoto, Kinoshita Shu-Ichi, Yamada Hiroaki S
KazumotoIguchi Research Laboratory, 70-3 Shinhari, Hari, Anan, Tokushima 774-0003, Japan.
J Theor Biol. 2007 Jul 7;247(1):138-51. doi: 10.1016/j.jtbi.2007.02.010. Epub 2007 Feb 28.
We studied 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 approximately 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 approximately 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 the existence of the transition at k(c)=2 derived in the annealed model.
我们研究了具有定向无标度网络的“淬火”考夫曼模型的布尔动力学，并将其与原始定向随机考夫曼网络以及定向指数波动网络的布尔动力学进行了比较。我们通过数值研究了状态循环长度的分布及其随网络规模N和节点平均度k增加的变化。在相对较小的网络（N约为150）中，对于k = 2的定向无标度网络和定向指数波动网络，中位数、平均值和标准差随N呈指数增长，其中分布的函数形式几乎为指数形式。我们发现，对于相对较大的N约为10³，随着平均度k变为k = 2，吸引子长度上分布中位数的增长渐近地从代数类型转变为指数类型。该结果支持了在退火模型中得出的k(c)=2处存在转变的结论。
