一类平面九次微分系统的广义中心条件与极限环分支（英文）  

General Center Conditions and Bifurcation of Limit Cycles for a Planar Differential System of Nine Degrees

作　　者：吴新民[1] 杜超雄[1] 

机构地区：[1]邵阳学院数学系,湖南邵阳422000

出　　处：《湘潭大学自然科学学报》2013年第3期9-14,共6页Natural Science Journal of Xiangtan University

基　　金：湖南省教育厅科研项目(09A082,11B113);湖南省自然科学基金项目(12JJ3008)

摘　　要：研究一类平面九次微分系统,通过两个合适的变换和焦点量的仔细计算,得到了无穷远点和4个初等奇点(-(1/2),((5±5(1/2))(3/2))/202(1/2)),(-(1/2),((-5(2(5-5(1/2))(1/2))+(10(5-5(1/2))(1/2)))/40),(-(1/2),((-5(2(5+5(1/2))(1/2))+(10(5+5(1/2))(1/2)))/40)同时成为五个广义中心的充要条件,进一步得到该系统在一定条件下能够同步分支出15个极限环,其中3个大振幅极限环来自无穷远点,12个小振幅极限环来自4个初等奇点.值得指出的是,相似的结论在已经出版的文献中未见.This paper is concerned with a class of planar differential system of nine degrees. By making two appropriate transformations of system and calculating focal values carefully1 we obtain the conditionsthat the infinity and four elementary loci become five general centers at the same time. Moreover 15 limitcycles including 12 small limit cycles from four elementary foci and 3 large limit cycles from the infinity can occur at the same step of disturbance under a certain condition. What is worth to mention is that similar con- clusions are hardly seen in published papers up till now and our work is new.

关 键 词：微分系统 极限环 广义中心 

分 类 号：O178[理学—数学]