{"title":"Hopf bifurcation in a class of piecewise smooth near-Hamiltonian systems","authors":"Maoan Han, Shanshan Liu","doi":"10.1016/j.bulsci.2024.103471","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we discuss Hopf bifurcation for planar piecewise smooth near-Hamiltonian systems with a center of parabolic-parabolic (PP) or focus-parabolic (FP) type. By studying asymptotic expansion of the first order Melnikov function, we obtain theorems to find an upper bound and a lower bound of the number of limit cycles near the center of these two types, respectively. Finally we provide two applications.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"195 ","pages":"Article 103471"},"PeriodicalIF":0.9000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449724000897","RegionNum":3,"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
In this paper, we discuss Hopf bifurcation for planar piecewise smooth near-Hamiltonian systems with a center of parabolic-parabolic (PP) or focus-parabolic (FP) type. By studying asymptotic expansion of the first order Melnikov function, we obtain theorems to find an upper bound and a lower bound of the number of limit cycles near the center of these two types, respectively. Finally we provide two applications.
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