一类三次微分系统的分段光滑扰动  

Piecewise smooth perturbation for a class of cubic differential systems

作　　者：李志鹏[1] 水树良[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2016年第3期258-262,共5页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11171309;11172269)

摘　　要：考虑了一类具有二次不变曲线的平面三次微分系统在分段三次多项式扰动下的极限环个数问题.利用一阶Melnikov函数,证明了从该系统的周期环域可以分支出8个极限环.结果表明:分段三次多项式扰动此类三次微分系统比其相应的三次多项式扰动可多产生4个极限环.It was studied the number of limit cycles that bifurcated from the periodic solutions of a cubic differ- ential system, when it was perturbed by piecewise cubic polynomials. By using first order Melnikov functions to this system, it was proved that 8 limit cycles were bifurcated from the period annulus. The result showed that piecewise cubic polynomials perturbation cubic differential system had 4 more limits cycles than corresponding cubic polynomials perturbation.

关 键 词：极限环 不变曲线 一阶Melnikov函数 分段光滑系统 

分 类 号：O175.25[理学—数学]