{"title":"Synchronization of discrete time Kuramoto oscillators with delayed states","authors":"Hua Zhang, Sisi Xiao","doi":"10.3934/dcdsb.2023183","DOIUrl":null,"url":null,"abstract":"This paper investigates the synchronization problem of a kind of discrete-time Kuramoto oscillators based on delayed position states. For this kind of Kuramoto model, the oscillators can only obtain delayed phase and frequency states relative to each other at a series of discrete time instants. Some simple sufficient conditions on the time step, the time delay, the natural frequencies, the coupling strength, and the historical and initial values of the phases and frequencies are derived analytically to ensure the phase synchronization of homogeneous oscillators and the frequency synchronization of heterogeneous oscillators, respectively. Finally, some numerical simulations are performed to verify the correctness of the theoretical results.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Continuous Dynamical Systems-Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcdsb.2023183","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper investigates the synchronization problem of a kind of discrete-time Kuramoto oscillators based on delayed position states. For this kind of Kuramoto model, the oscillators can only obtain delayed phase and frequency states relative to each other at a series of discrete time instants. Some simple sufficient conditions on the time step, the time delay, the natural frequencies, the coupling strength, and the historical and initial values of the phases and frequencies are derived analytically to ensure the phase synchronization of homogeneous oscillators and the frequency synchronization of heterogeneous oscillators, respectively. Finally, some numerical simulations are performed to verify the correctness of the theoretical results.
期刊介绍：
Centered around dynamics, DCDS-B is an interdisciplinary journal focusing on the interactions between mathematical modeling, analysis and scientific computations. The mission of the Journal is to bridge mathematics and sciences by publishing research papers that augment the fundamental ways we interpret, model and predict scientific phenomena. The Journal covers a broad range of areas including chemical, engineering, physical and life sciences. A more detailed indication is given by the subject interests of the members of the Editorial Board.
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