{"title":"可持续极限环存在性的判据。准则在Van der Pol方程一阶近似中的应用","authors":"K. Sheiretsky, S. Antonov","doi":"10.1109/ICEST52640.2021.9483481","DOIUrl":null,"url":null,"abstract":"The article proposes two criteria that the energy meets in order for the second-order differential equation to have a limit cycle and to be stable. The criteria were applied to establish the presence and stability of a limit cycle for the Van der Pol equation. Questions have been asked to be clarified using the method presented.","PeriodicalId":308948,"journal":{"name":"2021 56th International Scientific Conference on Information, Communication and Energy Systems and Technologies (ICEST)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Criteria for the Existence of a Sustainable Limit Cycle. Application of the Criteria in the First Approximation for the Van der Pol Equation\",\"authors\":\"K. Sheiretsky, S. Antonov\",\"doi\":\"10.1109/ICEST52640.2021.9483481\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The article proposes two criteria that the energy meets in order for the second-order differential equation to have a limit cycle and to be stable. The criteria were applied to establish the presence and stability of a limit cycle for the Van der Pol equation. Questions have been asked to be clarified using the method presented.\",\"PeriodicalId\":308948,\"journal\":{\"name\":\"2021 56th International Scientific Conference on Information, Communication and Energy Systems and Technologies (ICEST)\",\"volume\":\"15 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 56th International Scientific Conference on Information, Communication and Energy Systems and Technologies (ICEST)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICEST52640.2021.9483481\",\"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 56th International Scientific Conference on Information, Communication and Energy Systems and Technologies (ICEST)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICEST52640.2021.9483481","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文提出了二阶微分方程具有极限环和稳定的能量满足的两个判据。应用该准则建立了Van der Pol方程极限环的存在性和稳定性。已要求使用所提出的方法澄清问题。
Criteria for the Existence of a Sustainable Limit Cycle. Application of the Criteria in the First Approximation for the Van der Pol Equation
The article proposes two criteria that the energy meets in order for the second-order differential equation to have a limit cycle and to be stable. The criteria were applied to establish the presence and stability of a limit cycle for the Van der Pol equation. Questions have been asked to be clarified using the method presented.