Algebraic approach to the Kuramoto model.
basic_science · Level V
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- Record sourced from PubMed, PMID 34525516.
- Also identified by DOI 10.1103/PhysRevE.104.L022201.
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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, reformulations of nonlinear dynamics in higher-order number fields may provide tractable analytical approaches.