论文标题
在随机图上二阶库拉莫托模型中簇的稳定性
Stability of clusters in the second-order Kuramoto model on random graphs
论文作者
论文摘要
在这项工作中，分析了ERDOS-RENYYI图上具有惯性的耦合相振荡器的库拉莫托模型。对于从双峰分布采样固有频率的系统，我们确定了各种两个群集模式并研究其稳定性。为此，我们将群集动力学的描述分解为两个系统：一个管理两个集群质量中心的（宏）动力学，第二个管理每个集群中各个振荡器的（微）动力学。前者是低维的颂歌，而后者是两个耦合vlasov pdes的系统。群集动力学的稳定性取决于低维组运动的稳定性以及每个组中振荡器的相干性。我们表明，其中一个簇中的连贯性丧失导致两组状态的稳定性丧失和嵌合体状态的形成。可以将本文的分析推广到具有两个以上簇的状态，并在W-random图上耦合系统。我们的结果适用于具有波动源的电网模型。
The Kuramoto model of coupled phase oscillators with inertia on Erdos-Renyi graphs is analyzed in this work. For a system with intrinsic frequencies sampled from a bimodal distribution we identify a variety of two cluster patterns and study their stability. To this end, we decompose the description of the cluster dynamics into two systems: one governing the (macro) dynamics of the centers of mass of the two clusters and the second governing the (micro) dynamics of individual oscillators inside each cluster. The former is a low-dimensional ODE whereas the latter is a system of two coupled Vlasov PDEs. Stability of the cluster dynamics depends on the stability of the low-dimensional group motion and on coherence of the oscillators in each group. We show that the loss of coherence in one of the clusters leads to the loss of stability of a two-cluster state and to formation of chimera states. The analysis of this paper can be generalized to cover states with more than two clusters and to coupled systems on W-random graphs. Our results apply to a model of a power grid with fluctuating sources.
