On periodic perturbations of self-oscillating pendulum equations

In this paper we consider time-periodic perturbations of self-oscillating pendulum equation which arises from analysis of one system with two degrees of freedom. We derive averaged systems which describe the behavior of solutions of original equation in resonant areas and we find existence condition of Poincar homoclinic structure. In the case when autonomous equation has 5 limit cycles in oscillating region we give results of numerical computation. Under variation of perturbation frequency we investigate bifurcations of phase portraits of Poincar map.