Center Conditions and Bifurcation of Limit Cycles from the Equator for a Class of Cubic Polynomial Differential System

Studied in this paper are center conditions and bifurcation of limit cycles from the equator for a class of cubic polynomial system.By converting the real planar system into complex system,the recursion formula for the computation of singular quantities at infinity are given,and,with Mathemat- ica,the first 7 singular point quantities at infinity are deduced.At the same time,the condition for the infinity to be a center and 7 degree fine focus are derived,respectively.A cubic system that bifurcates 7 limit cycles from infinity is obtained.