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We study the existence of periodic solutions in a class of planar Filippovsystems obtained from non-autonomous periodic perturbations of reversiblepiecewise smooth differential systems. It is assumed that the unperturbedsystem presents a simple two-fold cycle, which is characterized by a closedtrajectory connecting a visible two-fold singularity to itself. It is shownthat under certain generic conditions the perturbed system has sliding andcrossing periodic solutions. In order to get our results, Melnikov's ideas wereapplied together with tools from the geometric singular perturbation theory.Finally, a study of a perturbed piecewise Hamiltonian model is performed.

Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a two-fold cycle