Emergent behaviors of the discrete-time Kuramoto model for generic initial configuration
Dynamical Systems
2019-09-10 v1
Abstract
In this paper, we will study the emergent dynamics of the discrete Kuramoto model for generic initial data. This is an extension of the previous work S.-Y. Ha et al. (2019), in which the initial configurations are supposed to be within a half circle. More precisely, we will provide the theory of discrete gradient flow which can be applied to general Euler iteration scheme. Therefore, as a direct application, we conclude the emergence of synchronization of discrete Kuramoto model. Moreover, we obtain for small mesh size that, the synchronization will occur exponentially fast for initial data in A_1 (see definition in (4.1)).
Cite
@article{arxiv.1909.03358,
title = {Emergent behaviors of the discrete-time Kuramoto model for generic initial configuration},
author = {Xiongtao Zhang and Tingting Zhu},
journal= {arXiv preprint arXiv:1909.03358},
year = {2019}
}