Abstract: In this paper, foe Melnikov function method has been used to analyse the distance between stable manifold and unstable manifold of the soft spring Duffing equation^[1] after its heteroclinic orbits rupture as the result of a small perturbation.The conditionsthat limit circles are bifurcated are given, and the their stability and location isdetermined.

Key words: limit circle, heteroclinic orbit, Melnikov function