The Bifurcation of Limit Cycles for a Planar Seventh Order Differential System
一类7次微分自治系统的极限环分支

In 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 $(\frac{1}{2},\frac{\sqrt{3}}{6}),(-\frac{1}{2},-\frac{\sqrt{3}}{6})$ 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.