On the Number of Limit Cycles Bifurcating from the Linear Center with an Algebraic Switching Curve

• Jiaxin Wang ^[1] ; Liqin Zhao ^[1] ; Jinping Zhou ^[1]
  1. [1] Beijing Normal University

     Beijing Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
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• Resumen

  • This paper studies the perturbations of system x˙=y, y˙=−x under arbitrary polynomial perturbations with switching curve y=xm, where m is a positive integer. By analysing the first order Melnikov function, we obtain the lower bound and upper bound of the maximum number of limit cycles bifurcating from the period annulus if the first order Melnikov function is not identically 0.