论文标题
库拉莫托振荡器的聚类同步和平均方法
Cluster Synchronization of Kuramoto Oscillators and the Method of Averaging
论文作者
论文摘要
提出了库拉莫托振荡器簇同步的严格条件。平均方法在稳定性分析中起重要作用，但是由于缺乏统一的连续性，标准Lyapunov的第二种方法不适用于。本文有助于通过非单调Lyapunov函数克服这一困难。我们平均稳定理论的扩展是得出两个相互关联的集群同步条件的关键：（i）群集之间的耦合强度足够弱，/或（ii）群集之间的固有频率在很大程度上是不同的。在没有网络分区的情况下，还研究了群集相位的凝聚力，以确保存在不变流形的存在。此外，我们将理论发现应用于大脑网络，并在网络参数和功能连接之间表现出一定的关系。
Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of uniform continuity. This paper contributes to overcoming this difficulty with the help of nonmonotonic Lyapunov functions. Our extensions of averaging in stability theory are key to derive the two interrelated cluster synchronization conditions: (i) the coupling strengths between clusters are sufficiently weak and/or (ii) the natural frequencies are largely different between clusters. Cluster phase cohesiveness in the absence of network partitions ensuring the existence of invariant manifolds is also investigated. Moreover, we apply our theoretical findings to brain networks and exhibit certain relations among network parameters and functional connectivity.
