A model of a generator of quasiperiodic oscillations forced by a periodic pulse sequence is studied. We analyze synchronization when the autonomous generator demonstrates periodic, quasiperiodic, respective weakly chaotic oscillations. For the forced quasiperiodic oscillations a picture of synchronization, consisting of small-scale and large-scale structures was uncovered. It even includes the existence of stable the three-frequency tori. For the regime of weak chaos a partial destruction of this features and of the regime of three-frequency tori are found.