Title: On mathematical analysis of synchronization to bidirectionally coupled Kuramoto oscillators
Authors: Chen, Shih-Hsin
Hsia, Chun-Hsiung
Shiue, Ming-Cheng
應用數學系
Department of Applied Mathematics
Keywords: Kuramoto;Synchronization;Bidirectionally coupled oscillators;Non all-to-all interaction
Issue Date: 1-Dec-2020
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 theta(i) only interacts with theta(i+1) and theta(i-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. (C) 2020 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.nonrwa.2020.103169
http://hdl.handle.net/11536/154898
ISSN: 1468-1218
DOI: 10.1016/j.nonrwa.2020.103169
Journal: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume: 56
Begin Page: 0
End Page: 0
Appears in Collections:Articles