Algebraic approach to the Kuramoto model

Authors

Lyle Muller, The University of Western OntarioFollow
Ján Mináč, The University of Western Ontario
Tung T. Nguyen, The University of Western Ontario

Document Type

Article

Publication Date

8-1-2021

Journal

Physical Review E

Volume

104

Issue

2

URL with Digital Object Identifier

10.1103/PhysRevE.104.L022201

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, reformulations of nonlinear dynamics in higher-order number fields may provide tractable analytical approaches.