Solutions with different periods bifurcated from a degenerate heteroclinic loop in a periodically perturbed system

We study solutions with different periods arising from a degenerate heteroclinic loop of type $ (d_{1}, d_{2}) $ under a single parametric perturbation. Although the existence of periodic solutions from homoclinic and heteroclinic bifurcations was well established in literature, the related multiplicity problem, i.e., determining the number of linearly independent bifurcating periodic solutions, is also interesting and needs to be investigated further. In this paper, we prove that $ d_{1}+d_{2} $ periodic solutions can arise via such a perturbation and give conditions for any integer $ n $ ($ 1\leq n\leq d_{1}+d_{2} $) under which $ n $ periodic solutions with different periods coexist.