{"title":"一类具有不稳定节点的四次微分系统的定性研究","authors":"R. Allaoua, R. Cheurfa, A. Bendjeddou","doi":"10.1109/ICRAMI52622.2021.9585912","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce a class of quartic differential system from the integrability and the existence of limit cycle. We show that this class is integrable and we give the explicit expression of first integral. After this, we prove, under suitable conditions on the parameters, that this class admits a non-algebraic limit cycle surrounding an unstable node. Concerning the singular points at infinity, we show that there is only one singular point. As an illustration, a phase portrait is drawn at the end of this paper.Mathematics Subject Classification: 34A05, 34C05, 34C07, 34C25.","PeriodicalId":440750,"journal":{"name":"2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Qualitative Study of a Class of Quartic Differential System with an Unstable Node\",\"authors\":\"R. Allaoua, R. Cheurfa, A. Bendjeddou\",\"doi\":\"10.1109/ICRAMI52622.2021.9585912\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce a class of quartic differential system from the integrability and the existence of limit cycle. We show that this class is integrable and we give the explicit expression of first integral. After this, we prove, under suitable conditions on the parameters, that this class admits a non-algebraic limit cycle surrounding an unstable node. Concerning the singular points at infinity, we show that there is only one singular point. As an illustration, a phase portrait is drawn at the end of this paper.Mathematics Subject Classification: 34A05, 34C05, 34C07, 34C25.\",\"PeriodicalId\":440750,\"journal\":{\"name\":\"2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICRAMI52622.2021.9585912\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICRAMI52622.2021.9585912","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Qualitative Study of a Class of Quartic Differential System with an Unstable Node
In this paper, we introduce a class of quartic differential system from the integrability and the existence of limit cycle. We show that this class is integrable and we give the explicit expression of first integral. After this, we prove, under suitable conditions on the parameters, that this class admits a non-algebraic limit cycle surrounding an unstable node. Concerning the singular points at infinity, we show that there is only one singular point. As an illustration, a phase portrait is drawn at the end of this paper.Mathematics Subject Classification: 34A05, 34C05, 34C07, 34C25.
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