Abstract: This paper deduces the formula of the third order Melnikov function. the relativc positions of the stable manifold and unstable manifold of the systems in electrical engineering are determined in supercritical cases, We make a comparison between the formulae of thesecond order Melnikov functions in[2] and[4] from studying of toral van der Pol equations)and find that the second order and the nth order formulae in[2] are wrong. Finaly,we correct this mistake.

Key words: hyperbolic saddle point, stable manifold, unstable manifold, homoclinic orbits, heleroclinic orbits