论文标题
图形上的平均野兔模型
Mean field Kuramoto models on graphs
论文作者
论文摘要
经典同步模型之一是库拉马托模型。我们使用离散的最佳传输动力学在图形上提出了一阶和二阶库拉莫托动力学模型。我们分析了图形上库拉莫托模型的一些示例的同步行为。我们还为离散的最佳运输系统提供了广义的Hopf-Cole转换。专注于两个点图，我们得出了具有熵功能引起的各种电势的库拉莫托动力学的分析公式。提出了库拉莫托模型在一般图上的几个数值示例。
One of a classical synchronization model is the Kuramoto model. We propose both first and second order Kuramoto dynamical models on graphs using discrete optimal transport dynamics. We analyze the synchronization behaviors for some examples of Kuramoto models on graphs. We also provide a generalized Hopf-Cole transformation for discrete optimal transport systems. Focus on the two points graph, we derive analytical formulas of the Kuramoto dynamics with various potential induced from entropy functionals. Several numerical examples for the Kuramoto model on general graphs are presented.
