Asymptotic behavior of the Kuramoto system with periodic natural frequency
type: Item
instance of: scholarly article
title: Asymptotic behavior of the Kuramoto system with periodic natural frequency
zbMATH Open document ID: 1489.34057
author: Sun-Ho Choi
author: Hyowon Seo
published in: Journal of Differential Equations
publication date: 2021-11-30T00:00:00Z
review text: The Kuramoto model is a fundamental and well-known model for studying synchronization of oscillators. This work studies an all-to-all coupled Kuramoto-type model \[\theta_i'=\omega_i(t)+\frac{K}{N}\sum_{k=1}^N \sin(\theta_k-\theta_i), \;\;\;1\leq i\leq N\] in which the natural frequencies \(\omega_i(t)\) of each of the oscillators varies periodically in time, with common period \(T\). Assuming that the coupling constant \(K\) is sufficeintly large, the authors prove the existence of a solution for which the differences \(\theta_i-\theta_j\) are \(T\)-periodic. The asymptotic behavior of the system is then characterized as the sum of a time-periodic solution, a drift term, and an exponentially decaying term. The theoretical results proved are illustrated by numerical simulations.
reviewed by: Guy Katriel
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 7436211
zbMATH Keywords: Kuramoto model
zbMATH Keywords: oscillations
zbMATH Keywords: asymptotic behavior
MaRDI profile type: Publication
full work available at URL: j.jde.2021.11.007
OpenAlex ID: W3212704853
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DOI: 10.1016/J.JDE.2021.11.007
description: scientific article; zbMATH DE number 7436211