{"title":"Global Hopf Bifurcation of State-Dependent Delay Differential Equations","authors":"Shangjiang Guo","doi":"10.1142/s0218127423500748","DOIUrl":null,"url":null,"abstract":"We apply the [Formula: see text]-equivariant degree method to a Hopf bifurcation problem for functional differential equations with a state-dependent delay. The formal linearization of the system at a stationary state is extracted and translated into a bifurcation invariant by using the homotopy invariance of [Formula: see text]-equivariant degree. As a result, the local Hopf bifurcation is detected and the global continuation of periodic solutions is described.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":" 635","pages":"2350074:1-2350074:13"},"PeriodicalIF":0.0000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Bifurc. Chaos","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218127423500748","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We apply the [Formula: see text]-equivariant degree method to a Hopf bifurcation problem for functional differential equations with a state-dependent delay. The formal linearization of the system at a stationary state is extracted and translated into a bifurcation invariant by using the homotopy invariance of [Formula: see text]-equivariant degree. As a result, the local Hopf bifurcation is detected and the global continuation of periodic solutions is described.