{"title":"由线性中心和无平衡点线性系统组成的一条直线分隔的不连续分段微分系统的显式非代数极限环","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":"{\"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}","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}
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
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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