Limit cycle problem for quadratic differential system x = -y + lx^2 + mxy, y =x(1 +ax +by)  

二次微分系统(x|·)=-y+lx^2+mxy,(y|·)=x(1+ax+by)的极限环问题(英文)

作　　者：陆炳新[1] 罗定军[1] 

机构地区：[1]南京师范大学数学与计算机科学学院,南京210097

出　　处：《Journal of Southeast University(English Edition)》2004年第4期517-520,共4页东南大学学报（英文版）

基　　金：TheNationalNaturalScienceFoundationofChina(No.19871041).

摘　　要：The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003,19(3):397-401) are corrected. By translating the system to be considered into the Lienard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue's paper mentioned above.研究了特殊Ⅲ类二次微分系统x=-Y+lx2+mxy,y=x(1+ax+by)的极限环的最大个数问题.纠正了索明霞和岳锡亭的文章(微分方程年刊,2003,19(3):397-401)中的一些错误.通过将所研究的系统化为Lienard型系统并利用其相关性质给出了几个定理,在某些条件下证明了系统最多存在2个极限环,改进了上述一文中的结果.

关 键 词：quadratic differential system limit cycle weak focus 

分 类 号：O175.12[理学—数学]