On the global convergence of frequency synchronization for Kuramoto and winfree oscillators
Journal
Discrete and Continuous Dynamical Systems - Series B
Journal Volume
24
Journal Issue
7
Pages
3319-3334
Date Issued
2019
Author(s)
Abstract
We investigate the collective behavior of synchrony for the Kuramoto and Winfree models. We first prove the global convergence of frequency synchronization for the non-identical Kuramoto system of three oscillators. It is shown that the uniform boundedness of the diameter of the phase functions implies complete frequency synchronization. In light of this, we show, under a suitable condition on the coupling strength and deviation of the intrinsic frequencies, that the diameter function of the phases is uniformly bounded. In a similar spirit, we also prove the global convergence of phase-locked synchronization for the Winfree model of N oscillators for N ≥ 2.
Type
journal article