Exponential synchronization of the high-dimensional Kuramoto model with identical oscillators under digraphs
Optimization and Control
2018-08-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1808.07263,
title = {Exponential synchronization of the high-dimensional Kuramoto model with identical oscillators under digraphs},
author = {Jinxing Zhang and Jiandong Zhu},
journal= {arXiv preprint arXiv:1808.07263},
year = {2018}
}
Comments
9 pages, 6 figures