English

An algebraic approach to the Kuramoto model

Dynamical Systems 2021-08-17 v3

Abstract

We study the Kuramoto model with attractive sine coupling. We introduce a complex-valued matrix formulation whose argument coincides with the original Kuramoto dynamics. We derive an exact solution for the complex-valued model, which permits analytical insight into individual realizations of the Kuramoto model. The existence of a complex-valued form of the Kuramoto model provides a key demonstration that, in some cases, re-formulations of nonlinear dynamics in higher-order number fields may provide tractable analytical approaches.

Cite

@article{arxiv.2105.04923,
  title  = {An algebraic approach to the Kuramoto model},
  author = {Lyle Muller and Ján Minác and Tung T. Nguyen},
  journal= {arXiv preprint arXiv:2105.04923},
  year   = {2021}
}

Comments

Published in Physical Review E, Volume. 104, No. 2

R2 v1 2026-06-24T01:58:59.072Z