Abstract: In this paper, we studied the exis tence problems of limit cycles of a class of Duffing equation x= y,y= x+y+xy. The bifurcation method was used to analyze the bifurcation after the homoclinic and periodic orbi t of the unperturbed sys tem was perturbed to break. The condi tions were given to ensure the generation of limit cycles.

Key words: duffing equation, homoclinic orbit, bifurcation, limit cycle