For the high-dimensional Kuramoto model with identical oscillators, the exponential synchronization has been proved and the exponential synchronization rate has been given. For the high-dimensional Kuramoto model with nonidentical oscillators, the sufficient and necessary conditions for complete phase synchronization have been obtained, but the problem of exponential synchronization has not been solved. In this paper, for the proportional -dimensional Kuramoto model, the matrix differential equations describing the synchronization error dynamics are constructed. When the interconnection graph is a strongly connected digraph, the local exponential synchronization rate is obtained.

中文翻译：

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比例[公式省略]维仓本振荡器的指数同步率

对于具有相同振子的高维Kuramoto模型，证明了指数同步并给出了指数同步率。对于非同质振子的高维Kuramoto模型，得到了完全相位同步的充分必要条件，但指数同步问题尚未解决。本文针对比例维Kuramoto模型，构造了描述同步误差动力学的矩阵微分方程。当互连图是强连通有向图时，获得局部指数同步率。