On mathematical analysis of synchronization to bidirectionally coupled Kuramoto oscillators
Journal
Nonlinear Analysis: Real World Applications
Journal Volume
56
Pages
-
Date Issued
2020
Author(s)
Abstract
This article is concerned about the synchronization problem of the bidirectionally coupled Kuramoto model. In this model, each oscillator only interacts with the oscillators with adjacent labeling numbers. Namely, the oscillator θi only interacts with θi+1 and θi−1. In real applications, this is a typical setting of concatenation connection. We first prove the global convergence of frequency synchronization for the identical oscillators. Also, we present two results of phase synchronization for the identical case in relatively wide initial configuration regimes. In the case that the coupling strength is sufficiently large (equivalent to the difference of the natural frequencies is sufficiently small), we show that for non-identical oscillators within a suitable initial configuration regime, the bidirectionally coupled Kuramoto model achieves a frequency synchronization. The supportive numerical simulations are presented as well.
Type
journal article