{"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 $\\end{document}</tex-math></inline-formula>, respectively. The results improve the conclusions in [<xref ref-type=\"bibr\" rid=\"b19\">19</xref>].</p>","PeriodicalId":435074,"journal":{"name":"Communications on Pure & Applied Analysis","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure & Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/cpaa.2022047","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper, we give an upper bound (for \begin{document}$ 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 $\end{document}, respectively. The results improve the conclusions in [19].
In this paper, we give an upper bound (for \begin{document}$ 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].
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