无标度复杂网络中吸引子态的鲁棒性
Robustness of Attractor States in Complex Networks with Scale-free Topology
摘要：
研究了具有无标度拓扑结构的复杂网络中布尔动力学吸引子的内在性质，并与随机Kauffman网络进行了比较。我们数值研究了冻结和相关节点的每个吸引子，和吸引子的鲁棒性的扰动，翻转的状态的一个节点的吸引子在相对较小的网络（$N=30 \sim 200$）。结果表明，在无标度拓扑结构的复杂网络中，冻结节点的比率大于随机Kauffman模型中的冻结节点比率。此外，我们还发现，在复杂的无标度网络的度数波动的吸引子是更敏感的状态翻转的高度连接的节点比一个连接较少的节点的状态翻转。
英文摘要：
We study the intrinsic properties of attractors in the Boolean dynamics in complex network with scale-free topology, comparing with those of the so-called random Kauffman networks. We have numerically investigated the frozen and relevant nodes for each attractor, and the robustness of the attractors to the perturbation that flips the state of a single node of attractors in the relatively small network ($N=30 \sim 200$). It is shown that the rate of frozen nodes in the complex networks with scale-free topology is larger than that in the random Kauffman model. Furthermore, we have found that in the complex scale-free networks with fluctuations of in-degree number the attractors are more sensitive to the state flip of a highly connected node than to the state flip of a less connected node.
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