一类7次微分自治系统的极限环分支  

THE BIFURCATION OF LIMIT CYCLES FOR A PLANAR SEVENTH ORDER DIFFERENTIAL SYSTEM

作　　者：杜超雄[1,2] 米黑龙[3] 陈海波[2] 

机构地区：[1]邵阳学院数学系,邵阳422000 [2]中南大学数学院,长沙410083 [3]湖南商学院信息科学系,长沙410083

出　　处：《系统科学与数学》2010年第10期1386-1398,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11071222;10871206);湖南省教育厅重点(09A082)资助课题

摘　　要：研究一类平面7次微分系统,通过作两个适当的变换以及焦点量的仔细计算,得出了系统的无穷远点与2个初等焦点能够同时成为广义细焦点的条件,进一步得出在一定条件下该系统能够分支出15个极限环的结论,其中5个大振幅极限环来自无穷远点,10个小振幅极限环来自2个初等焦点.this paper,a class of planar seventh order differential system is investigated. By introducing two appropriate transformations of system and calculating general focal values carefully,the infinity and two elementary focuses（1/2,3^（1/2）/6）,（-1/2,-3^（1/2）/6） become three general 5th fine foci at the same time and moreover 15 limit cycles including 10 small limit cycles from two elementary focuses and 5 large limit cycles from the infinity can occur under a certain condition.

关 键 词：Bendixson同胚变换 广义焦点量 极限环 分支 

分 类 号：O153.3[理学—数学]