Algebraic approach to the Kuramoto model
Lyle Muller, Ján Mináč, Tung T. Nguyen
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.
Topics & Concepts
Kuramoto modelNonlinear systemSineStatistical physicsCoupling (piping)MathematicsComplex systemArgument (complex analysis)Matrix (chemical analysis)Computer scienceAlgebraic numberApplied mathematicsSynchronization (alternating current)Topology (electrical circuits)Mathematical analysisPhysicsArtificial intelligenceGeometryCombinatoricsEngineeringQuantum mechanicsChemistryComposite materialBiochemistryMechanical engineeringMaterials scienceNonlinear Dynamics and Pattern FormationTheoretical and Computational PhysicsComplex Systems and Time Series Analysis