Relevant elements, magnetization and dynamical properties in Kauffman networks: A numerical study
Relevant elements, magnetization and dynamical properties in Kauffman networks: A numerical study
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DOI：
10.1016/s0167-2789(97)00243-1
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发表时间：
1998-05-01
影响因子：
4
通讯作者：
Parisi, G
中科院分区：
文献类型：
--
作者：
Bastolla, U;Parisi, G
这是关于考夫曼网络结构的两篇论文中的第一篇。本文在Flyvbjerg [J.Phys.A21（1988）L955-L960]及Flyvbjerg和Kjaer [J.Phys.A21（1988）1695-1718]的工作基础上，定义了自动机随机网络的有关元素，并数值研究了它们在混沌相和临界线上的概率分布。一个简单的近似参数预测，它们的数量尺度为根N的临界线上，而它是线性的N在混沌阶段和冻结阶段的系统大小无关。数值结果证实了这一论点。相关元素的研究提供了有用的信息，在临界网络中的吸引子的性质，其中来自近似计算方法或模拟的图片是不是很清楚。版权所有（C）1998 Elsevier Science B. V.
This is the first of two papers about the structure of Kauffman networks. In this paper we define the relevant elements of random networks of automata, following previous work by Flyvbjerg [J. Phys. A 21 (1988) L955-L960] and Flyvbjerg and Kjaer [J. Phys. A 21 (1988) 1695-1718], and we study numerically their probability distributions in the chaotic phase and on the critical line of the model. A simple approximate argument predicts that their number scales as root N on the critical line, while it is linear with N in the chaotic phase and independent on system size in the frozen phase. This argument is confirmed by numerical results. The study of the relevant elements gives useful information about the properties of the attractors in critical networks, where the pictures coming from either approximate computation methods or from simulations are not very clear. Copyright (C) 1998 Elsevier Science B.V.