Exact solution of Kauffman's model with connectivity one
Exact solution of Kauffman's model with connectivity one
复制标题
具有连通性的考夫曼模型的精确解一
DOI：
10.1088/0305-4470/21/7/031
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
N. Kjr
中科院分区：
文献类型：
--
作者：
H. Flyvbjerg;N. Kjr
考夫曼的模型是布尔自动机的随机组合网络。每个自动机接收来自最多K个其他自动机的输入。它在离散时间t+1的状态由时间t的K个输入的随机选择但固定的布尔函数确定。由此产生的淬火，网络的随机动力学演示了两个阶段：冻结和混沌阶段。作者给出了一个精确的解决方案，该模型的连通性K=1，有效的任何地方，在冻结阶段和临界点，有效的有限以及无限的网络。他们讨论了网络的临界行为和有限尺寸效应。冷冻阶段的结果提出了补充最近的精确结果为K=无穷大的混沌阶段。
Kauffman's model is a randomly assembled network of Boolean automata. Each automaton receives inputs from at most K other automata. Its state at discrete time t+1 is determined by a randomly chosen, but fixed, Boolean function of the K inputs at time t. The resulting quenched, random dynamics of the network demonstrates two phases: a frozen and a chaotic phase. The authors give an exact solution of the model for connectivity K=1, valid everywhere in the frozen phase and at a critical point, valid for finite as well as for infinite networks. They discuss the network's critical behaviour and finite-size effects. The results for the frozen phase presented complement recent exact results for the chaotic phase obtained for K= infinity .