Semidefinite Programming Certificates for Synchronization of Kuramoto Oscillators on Arcs
arXiv:2606.03591
Abstract
A class of Kuramoto models with a general coupling function that can be expressed in terms of a finite number of harmonics, each comprising sinusoidal terms, is studied. We propose a novel approach for certifying local phase synchronization in this class for all initial conditions lying on an arc. The trace parametrization property and Gram matrix representation of a trigonometric polynomial are utilized along with Putinar's Positivstellensatz to obtain semidefinite programming certificates for the stability of the phase-difference system, which in turn implies synchronization of the original system. The results can be extended to any system of coupled oscillators where the forward-invariance on arcs can be established.
A version of this work has been accepted for publication in Chaos and Complex Systems: Proceedings of the 6th International Interdisciplinary Chaos Symposium