{"title":"具有两条切换线的二次等时系统摄动的极限环数","authors":"Ai Ke, Maoan Han, Wei-Jian Geng","doi":"10.3934/cpaa.2022047","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we give an upper bound (for <inline-formula><tex-math id=\"M1\">\\begin{document}$ n\\geq3 $\\end{document}</tex-math></inline-formula>) and the least upper bound (for <inline-formula><tex-math id=\"M2\">\\begin{document}$ n = 1,2 $\\end{document}</tex-math></inline-formula>) of the number of limit cycles bifurcated from period annuli of a quadratic isochronous system under the piecewise polynomial perturbations of degree <inline-formula><tex-math id=\"M3\">\\begin{document}$ n $\\end{document}</tex-math></inline-formula>, respectively. The results improve the conclusions in [<xref ref-type=\"bibr\" rid=\"b19\">19</xref>].</p>","PeriodicalId":435074,"journal":{"name":"Communications on Pure & Applied Analysis","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The number of limit cycles from the perturbation of a quadratic isochronous system with two switching lines\",\"authors\":\"Ai Ke, Maoan Han, Wei-Jian Geng\",\"doi\":\"10.3934/cpaa.2022047\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p style='text-indent:20px;'>In this paper, we give an upper bound (for <inline-formula><tex-math id=\\\"M1\\\">\\\\begin{document}$ n\\\\geq3 $\\\\end{document}</tex-math></inline-formula>) and the least upper bound (for <inline-formula><tex-math id=\\\"M2\\\">\\\\begin{document}$ n = 1,2 $\\\\end{document}</tex-math></inline-formula>) of the number of limit cycles bifurcated from period annuli of a quadratic isochronous system under the piecewise polynomial perturbations of degree <inline-formula><tex-math id=\\\"M3\\\">\\\\begin{document}$ n $\\\\end{document}</tex-math></inline-formula>, respectively. The results improve the conclusions in [<xref ref-type=\\\"bibr\\\" rid=\\\"b19\\\">19</xref>].</p>\",\"PeriodicalId\":435074,\"journal\":{\"name\":\"Communications on Pure & Applied Analysis\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications on Pure & Applied Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/cpaa.2022047\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure & Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/cpaa.2022047","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
In this paper, we give an upper bound (for \begin{document}$ n\geq3 $\end{document}) and the least upper bound (for \begin{document}$ n = 1,2 $\end{document}) of the number of limit cycles bifurcated from period annuli of a quadratic isochronous system under the piecewise polynomial perturbations of degree \begin{document}$ n $\end{document}, respectively. The results improve the conclusions in [19].
The number of limit cycles from the perturbation of a quadratic isochronous system with two switching lines
In this paper, we give an upper bound (for \begin{document}$ n\geq3 $\end{document}) and the least upper bound (for \begin{document}$ n = 1,2 $\end{document}) of the number of limit cycles bifurcated from period annuli of a quadratic isochronous system under the piecewise polynomial perturbations of degree \begin{document}$ n $\end{document}, respectively. The results improve the conclusions in [19].