A new method to produce limit cycles in a near-Hamiltonian system

As is well known, there have been extensive studies on the bifurcation of limit cycles for near-Hamiltonian systems. In this paper, we provide a new method to produce limit cycles near a class of heteroclinic loops with two or three saddles. More precisely, we perturb the polycycle to form a perturbed 2-polycycle and then produce limit cycles by changing the stability of the perturbed 2-polycycle. We also present two examples as applications, which demonstrate the advantages of our new method.