An algebraic approach to the Kuramoto model

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.

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

References in corpus (1)

• A linear reformulation of the Kuramoto model of self-synchronizing oscillators

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