Explicit Non Algebraic Limit Cycle for a Discontinuous Piecewise Differential Systems Separated by One Straight Line and Formed by Linear Center and Linear System Without Equilibria
{"title":"Explicit Non Algebraic Limit Cycle for a Discontinuous Piecewise Differential Systems Separated by One Straight Line and Formed by Linear Center and Linear System Without Equilibria","authors":"A. Berbache","doi":"10.2478/tmmp-2021-0019","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we deal with the discontinuous piecewise differential linear systems formed by two differential systems separated by a straight line when one of these two differential systems is a linear without equilibria and the other is a linear center. We are going to show that the maximum number of crossing limit cycles is one, and if exists, it is non algebraic and analytically given.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"79 1","pages":"47 - 58"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tatra Mountains Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/tmmp-2021-0019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
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Abstract
Abstract In this paper, we deal with the discontinuous piecewise differential linear systems formed by two differential systems separated by a straight line when one of these two differential systems is a linear without equilibria and the other is a linear center. We are going to show that the maximum number of crossing limit cycles is one, and if exists, it is non algebraic and analytically given.
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