Extracting topological features from dynamical measures in networks of Kuramoto oscillators.
Extracting topological features from dynamical measures in networks of Kuramoto oscillators.
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DOI：
10.1103/physreve.85.036112
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发表时间：
2011-02
期刊：
影响因子：
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通讯作者：
L. Prignano;A. Díaz-Guilera
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文献类型：
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作者：
L. Prignano;A. Díaz-Guilera
耦合振子系综的Kuramoto模型提供了非相干态和同步态之间非平衡跃迁的范例。在这里，我们分析了任意相互作用网络中几乎相同的振子群。我们的目的是从纯粹的动力学度量中提取连通性模式的拓扑特征，这是基于这样一个事实，即在异质网络中，全球动力学不仅受自然频率的分布的影响，而且还受不同值的位置的影响。为了进行定量研究，我们将重点放在一个非常简单的频率分布上，考虑到除了起搏器节点的一个频率外，所有频率都是相等的。然后，我们分析了当系统处于高度非相干态时，系统在过渡点、略高于临界点以及远离临界点时的动力学行为。收集的拓扑信息范围从局部特征，如单节点连通性，到功能簇的层次结构，甚至到整个邻接矩阵。
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of nonequilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in arbitrary interaction networks. Our aim is to extract topological features of the connectivity pattern from purely dynamical measures based on the fact that in a heterogeneous network the global dynamics is not only affected by the distribution of the natural frequencies but also by the location of the different values. In order to perform a quantitative study we focused on a very simple frequency distribution considering that all the frequencies are equal but one, that of the pacemaker node. We then analyze the dynamical behavior of the system at the transition point and slightly above it as well as very far from the critical point, when it is in a highly incoherent state. The gathered topological information ranges from local features, such as the single-node connectivity, to the hierarchical structure of functional clusters and even to the entire adjacency matrix.