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arXiv · 2105.04923

An algebraic approach to the Kuramoto model

Lyle Muller·Ján Minác·Tung T. Nguyen
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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.

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Lyle Muller, Ján Minác, Tung T. Nguyen. 2021-05-11. An algebraic approach to the Kuramoto model. https://doi.org/10.1103/physreve.104.l022201

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