2018/08/22 by Jinxing Zhang, Zhang, Jinxing, Jiandong Zhu +1
Computer Science · Engineering · #FOS: Mathematics #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.1808.07263
openalex publication_date 2018/08/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
For the Kuramoto model and its variations, it is difficult to analyze the exponential synchronization under the general digraphs due to the lack of symmetry. %due to the asymmetry of the adjacency matrices. In this paper, for the high-dimensional Kuramoto model of identical oscillators, a matrix Riccati differential equation (MRDE) is proposed to describe the error dynamics. Based on the MRDE, the exponential synchronization is proved by constructing a total error function for the case of digraphs admitting spanning trees. Finally, some numerical simulations are given to illustrate the obtained theoretical results.