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摘要翻译：
我们证明了要正确描述Kauffman随机布尔网络中临界线的位置，必须考虑损伤扩展过程中的渗流现象。由于随机无向网络中的渗流跃迁问题比有向网络中的渗流跃迁问题简单得多，我们研究了无向网络中的Kauffman模型。我们导出了这些网络巨分量临界线的平均场公式，并证明了表征整个网络的临界线是小团簇的有序行为屏蔽巨分量的混沌行为的结果。我们还对屏蔽效应的解析描述提出了一种可能的态度。本文给出的理论推导结果与经典随机图的数值模拟结果是一致的。
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英文标题：
《Critical line in undirected Kauffman boolean networks - the role of
percolation》
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作者：
Piotr Fronczak, Agata Fronczak
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We show that to correctly describe the position of the critical line in the Kauffman random boolean networks one must take into account percolation phenomena underlying the process of damage spreading. For this reason, since the issue of percolation transition is much simpler in random undirected networks, than in the directed ones, we study the Kauffman model in undirected networks. We derive the mean field formula for the critical line in the giant component of these networks, and show that the critical line characterizing the whole network results from the fact that the ordered behavior of small clusters shields the chaotic behavior of the giant component. We also show a possible attitude towards the analytical description of the shielding effect. The theoretical derivations given in this paper quite tally with numerical simulations done for classical random graphs.
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PDF链接：
https://arxiv.org/pdf/712.0882
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