Abstract:

 This paper considers the bifurcation of limit cycle of a class of cubic system with two imaginary invariant line, and  gives the focus valus of each order at O(0,0). It is proved that the system with δlmn=0  has at most one limit cycle surrounding O. With the bifurcation theory, the authors  give the bifurcation curve of homoclinic cycle and semistable cycle. It means that the system has at  most two limit cycles surrounding O

Key words: Invariant line, Cubic system, Bifurcation, Limit cycle; , Uniqueness