Bifurcation of limit cycles near heteroclinic loops in near-Hamiltonian systems (Q2219605)

In this paper, a method for calculating the expansion coefficients of the first order Melnikov function is proposed, which is suitable for the near-Hamiltonian system near the polycycle with hyperbolic saddles. With more those coefficients, more limit cycles could be determined around the polycycle. The limit cycles generated from a heteroclinic cycle with two saddles is taken as an example to illustrate the method. The result is new and interesting.