一类不连续平面二次微分系统的极限环  

Limit cycles for a class of discontinuous planar quadratic differential system

作　　者：李时敏[1] 赵育林[2] 岑秀丽 

机构地区：[1]广东财经大学数学与统计学院,广州510320 [2]中山大学数学与计算科学学院,广州510275

出　　处：《中国科学：数学》2015年第1期43-52,共10页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11171355和11401111);广东财经大学校级课题(批准号:13YB11001)资助项目

摘　　要：本文考虑了一类不连续平面二次可积非Hamilton微分系统在二次扰动下的极限环个数问题.利用一阶平均法,我们得到了从该系统中心的周期环域至少可以分支出5个极限环的结论.该结果表明不连续二次微分系统比其相应光滑微分系统至少可以多分支出2个极限环.In this paper, we consider the number of limit cycles for a class of discontinuous planar quadratic integrable non-Hamiltonian system under quadratic perturbation. Using the first order averaging method, we obtain that there are at least 5 limit cycles which can bifurcate from the period annulus of the center for this system. Our result also shows that the discontinuous quadratic system can have at least 2 more limit cycles than the smooth one.

关 键 词：极限环 平均法 不连续微分系统 

分 类 号：O175[理学—数学]