论文标题
动态随机图的库拉莫托模型
The Kuramoto model on dynamic random graphs
论文作者
论文摘要
我们在随着时间的变化图上提出了一个耦合振荡器的库拉莫托模型，该图的动力学是由图形空间中的马尔可夫过程决定的。最简单的代表正在考虑基本图，然后考虑由$ n $独立的随机步行在基础图上确定的子图。我们证明了从相位粘附组开始的解决方案的同步结果，独立于随机步行者的速度，平均原理和全局同步结果，具有足够快速的过程的可能性。我们还考虑了随机电导模型的动态版本中的库拉莫托振荡器。
We propose a Kuramoto model of coupled oscillators on a time-varying graph, whose dynamics is dictated by a Markov process in the space of graphs. The simplest representative is considering a base graph and then the subgraph determined by $N$ independent random walks on the underlying graph. We prove a synchronization result for solutions starting from a phase-cohesive set independent of the speed of the random walkers, an averaging principle and a global synchronization result with high probability for sufficiently fast processes. We also consider Kuramoto oscillators in a dynamical version of the Random Conductance Model.
