Dynamic pattern evolution on scale-free networks.
Dynamic pattern evolution on scale-free networks.
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DOI：
10.1073/pnas.0409296102
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发表时间：
2005-07
影响因子：
11.1
通讯作者：
Haijun Zhou;R. Lipowsky
中科院分区：
文献类型：
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作者：
Haijun Zhou;R. Lipowsky
用解析方法和计算机仿真方法研究了一类一般的无标度网络动态模型。每个网络由N个顶点组成，其度分布P(K)表示随机选择的顶点连接到k个最近邻点的概率。每个顶点可以获得两个内部状态，由二元变量或类伊辛自旋描述，这些自旋根据局部多数规则随时间演化。无标度网络的度分布具有约为k(-伽马)的幂定律尾部P(K)，它对伽马5/2表现出本质上不同的动态行为，这揭示了许多真实世界的网络是2 5/2的无标度网络的经验观察，另一方面，这种衰减时间发散为ln(N)与网络大小N。对于包括联想记忆网络的Hopfield模型在内的各种更复杂的模型，也发现了类似的区别。在后一种情况下，在平均场理论中发现，在伽马5/2的大N限制下，存储容量与N无关，但对于2<；伽马5/2，存储容量增长为N(α)，其中α=(5-2伽马)/(伽马-1)。
A general class of dynamic models on scale-free networks is studied by analytical methods and computer simulations. Each network consists of N vertices and is characterized by its degree distribution, P(k), which represents the probability that a randomly chosen vertex is connected to k nearest neighbors. Each vertex can attain two internal states described by binary variables or Ising-like spins that evolve in time according to local majority rules. Scale-free networks, for which the degree distribution has a power law tail P(k) approximately k(-gamma), are shown to exhibit qualitatively different dynamic behavior for gamma 5/2, shedding light on the empirical observation that many real-world networks are scale-free with 2 5/2, on the other hand, this decay time diverges as ln(N) with the network size N. An analogous distinction is found for a variety of more complex models including Hopfield models for associative memory networks. In the latter case, the storage capacity is found, within mean field theory, to be independent of N in the limit of large N for gamma > 5/2 but to grow as N(alpha) with alpha = (5 - 2gamma)/(gamma - 1) for 2 < gamma < 5/2.