• 论文 •

### 一类七次多项式微分系统的中心条件与赤道极限环分支

1. 中南大学数学科学与计算技术学院,长沙 410075
• 收稿日期:2006-03-28 修回日期:2006-11-13 出版日期:2008-03-25 发布日期:2008-03-25

ZHANG Qi;LIU Yirong. Center Conditions and Bifurcation of Limit Cycles at the Equatorin a Class of Seven Degree Polynomial Differential System[J]. Journal of Systems Science and Mathematical Sciences, 2008, 28(3): 275-281.

### Center Conditions and Bifurcation of Limit Cycles at the Equatorin a Class of Seven Degree Polynomial Differential System

ZHANG Qi, LIU Yirong

1. School of Mathematical Science and Computing Technology, Central South University, Changsha 410075
• Received:2006-03-28 Revised:2006-11-13 Online:2008-03-25 Published:2008-03-25

Center conditions and bifurcation of limit cycles from the equator in a class of polynomial system of degree seven are studied. By converting real planar system into complex system, the recursion formula for the computation of singular point quantities of the infinity are given, and with computer algebra system Mathematica, the first 14 singular point quantities of the infinity are deduced.
At the same time, the conditions for the infinity to be a center and 14 degree fine focus are derived respectively. According to the above, a system of degree seven that bifurcates 12 limit cycles from the infinity is constructed.

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