English

Emergence of synchronization in Kuramoto model with general digraph

Dynamical Systems 2021-07-15 v1

Abstract

In this paper, we study the complete synchronization of the Kuramoto model with general network containing a spanning tree, when the initial phases are distributed in an open half circle. As lack of uniform coercivity in general digraph, in order to capture the dissipation structure on a general network, we apply the node decomposition criteria in \cite{H-L-Z20} to yield a hierarchical structure, which leads to the hypo-coercivity. This drives the phase diameter into a small region after finite time in a large coupling regime, and the uniform boundedness of the diameter eventually leads to the emergence of exponentially fast synchronization.

Keywords

Cite

@article{arxiv.2107.06487,
  title  = {Emergence of synchronization in Kuramoto model with general digraph},
  author = {Xiongtao Zhang and Tingting Zhu},
  journal= {arXiv preprint arXiv:2107.06487},
  year   = {2021}
}
R2 v1 2026-06-24T04:10:45.233Z