一类平面微分系统的广义中心条件与极限环分支  

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

作　　者：杜超雄[1] 刘一戎[2] 

机构地区：[1]邵阳学院数学系,邵阳422004 [2]中南大学数学与统计学学院,长沙410083

出　　处：《应用数学学报》2014年第1期69-77,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11261013;11371373);湖南省科技厅计划项目(2012FJ3106)资助项目

摘　　要：本文研究一类平面微分系统,通过作两个适当的变换以及焦点量的仔细计算,得出了该系统的无穷远点与5个初等奇点(-1/2,0),(-1/2,±3^(1/2)/2),(±1/2,-3^(1/2)/6)能够同时成为6个广义中心的条件,进一步得出在一定条件下该系统能够分支出12个极限环的结论,其中2个大振幅极限环来自无穷远点,10个小振幅极限环来自5个初等焦点.我们的工作是有意义的,相似的结论在已经出版的文献中少见。This paper is concerned with a class of planar differential system of nine de- grees.By making two appropriate transformations of system and calculating focal values care- （-？,0）,（-？, ±√3/2） fully, we obtain the conditions that the infinity and five elementary foci（-？,0）（-？,√3/2± become six general centers at the same time.Moreover 12 limit cycles including 10 small limit cycles from five elementary loci and 2 large limit cycles from the infinity can occur at the same step of disturbance under a certain condition.What is worth mentioning is that similar conclusions have hardly been seen in published paper up till now and our work is significative.

关 键 词：广义等变系统 广义焦点量 极限环 广义中心 

分 类 号：O175.12[理学—数学]