Predicting Criticality and Dynamic Range in Complex Networks: Effects of Topology
Predicting Criticality and Dynamic Range in Complex Networks: Effects of Topology
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DOI：
10.1103/physrevlett.106.058101
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发表时间：
2011-01-31
影响因子：
8.6
通讯作者：
Restrepo, Juan G.
中科院分区：
文献类型：
--
作者：
Larremore, Daniel B.;Shew, Woodrow L.;Restrepo, Juan G.
耦合可兴奋系统网络响应外部刺激的集体动态取决于网络中连接的拓扑结构。在这里，我们开发了一个通用的理论方法来研究网络拓扑结构对动态范围的影响，它量化的范围内的刺激强度导致可区分的网络反应。我们发现加权网络邻接矩阵的最大特征值决定了网络的动态范围。当最大特征值恰好为1时，系统处于临界状态，其动态范围最大。此外，我们还研究了稳态系统的高阶行为，它预测具有更均匀度分布的网络应该具有更高的动态范围。我们的分析，证实了数值模拟，概括了以前的研究中的邻接矩阵的最大特征值。
The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. When the largest eigenvalue is exactly one, the system is in a critical state and its dynamic range is maximized. Further, we examine higher order behavior of the steady state system, which predicts that networks with more homogeneous degree distributions should have higher dynamic range. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.