一个三次等时中心在非光滑扰动下的极限环分支

LIMIT CYCLES BIFURCATION FROM A CUBIC ISOCHRONOUS CENTER UNDER NON-SMOOTH PERTURBATIONS

本文研究了一个三次等时中心在非光滑扰动下的极限环分支问题.利用非光滑系统的一阶平均方法,获得了在任意小的分段三次多项式扰动下,从未扰动系统的周期环域中至多分支出7个极限环,而且此上界可以达到,推广了光滑扰动下的结果.

This paper is devoted to study the bifurcation of limit cycles from a cubic isochronous center under any small non-smooth perturbations.By using the averaging theory for discontinuous differential systems,it proves that under any small piecewise cubic polynomial perturbations,at most seven limit cycles bifurcate from the period annulus sounding the center of the unperturbed system,and this upper bound can be reached,which extends the resultant under smooth perturbations.