Calculated On The Amount Of Homoclinic Bifurcation Boundaries

The paper includes four parts. In the first part, the latest progresses and some important results about the bifurcation theory of planar dynamical systems are stated ;In the second part, by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle, the exact computation formula of h3(T) for the multiple limit cycle bifurcation for a given system is given; In the third part , proof of the convergence of h3(T) as Tâ†'∞ is shown; At the last part , a computation formula for higher separatrix values(k > 3) is conjectured.