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  • Letter
  • Open Access

Algebraic approach to the Kuramoto model

Lyle Muller*, Ján Mináč, and Tung T. Nguyen

  • Department of Mathematics, Western University, London, Ontario, Canada N6A 3K7

  • *Corresponding author: lmuller2@uwo.ca
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Phys. Rev. E 104, L022201 – Published 5 August, 2021

DOI: https://doi.org/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.

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Phys. Rev. E 104, L022201– Published 5 August, 2021
  • Received 21 February 2021
  • Revised 11 May 2021
  • Accepted 17 June 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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