从Kuramoto振子网络的动力学测度中提取拓扑特征
Extracting topological features from dynamical measures in networks of Kuramoto oscillators
摘要：
耦合振子系综的仓本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，我们分析人口几乎相同的振荡器在任意相互作用网络。我们的目标是提取拓扑特征的连接模式从纯粹的动态措施，基于这样一个事实，即在一个异构的网络的全球动态不仅受分布的固有频率，但也由不同的值的位置。为了进行定量研究，我们集中在一个非常简单的频率分布，考虑到所有的频率是相等的，但一个，起搏器节点。然后，我们分析了系统的动力学行为在过渡点和略高于它，以及非常远离临界点，当它是在一个高度不相干的状态。收集的拓扑信息范围从局部特征，如单个节点的连通性，功能集群的层次结构，甚至整个邻接矩阵。
英文摘要：
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium 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.
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