On Exponential Synchronization Rates for High-Dimensional Kuramoto Models With Identical Oscillators and Digraphs

• 成果类型: Article
• 署名作者: Peng, Shanshan; Zhang, Jinxing; Zhu, Jiandong; Lu, Jianquan; Li, Xiaodi
• 署名单位: Southeast University - China; Shandong Normal University; Nanjing Normal University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3144942
• 发表日期: 2023
• 页码: 1054-1060
• 关键词: Synchronization; mathematical models; Symmetric matrices; MANIFOLDS; Laplace equations; Eigenvalues and eigenfunctions; oscillators; directed graph; exponential synchronization rate; high-dimensional Kuramoto model

摘要

For a high-dimensional Kuramoto model with identical oscillators under a general digraph that has a directed spanning tree, although the exponential synchronization has been proved under some initial state constraints, exponential synchronization rates have not been described exactly until now. In this article, the supremum of exponential synchronization rates is precisely determined as the smallest real part of the nonzero Laplacian eigenvalues of the digraph. Our obtained result extends the existing results from the special case of strongly connected balanced digraphs to the condition of general digraphs owning directed spanning trees, which is the weakest condition for synchronization from the aspect of network structure. Moreover, our adopted method is completely different from and much more elementary than the previous differential geometry method.