Centers and limit cycles of polynomial differential systems of degree via averaging theory

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• 作者：Rebiha Benterki^a ; ^{r-benterki@yahoo.fr" class="auth_mail" title="E-mail the corresponding author} ; Jaume Llibre^b ; ^{jllibre@mat.uab.cat" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 34C15 ; 34C25
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：273-283
• 全文大小：478 K

文摘

In this paper we classify the phase portraits in the Poincaré disc of the centers of the generalized class of Kukles systems symmetric with respect to the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304162&_mathId=si51.gif&_user=111111111&_pii=S0377042716304162&_rdoc=1&_issn=03770427&md5=05b056347df020542a616e50005b2b62" title="Click to view the MathML source">yclass="mathContainer hidden">class="mathCode">$y$-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304162&_mathId=si49.gif&_user=111111111&_pii=S0377042716304162&_rdoc=1&_issn=03770427&md5=d2087ee5f26ef55f6e57e943dcf1c590" title="Click to view the MathML source">4class="mathContainer hidden">class="mathCode">$4$.