  In this paper we present an influence of discontinuous coupling on the
dynamics of multistable systems. Our model consists of two periodically forced
oscillators that can interact via soft impacts. The controlling parameters are
the distance between the oscillators and the difference in the phase of the
harmonic excitation. When the distance is large two systems do not collide and
a number of different possible solutions can be observed in both of them. When
decreasing of the distance, one can observe some transient impacts and then the
systems settle down on non-impacting attractor. It is shown that with the
properly chosen distance and difference in the phase of the harmonic
excitation, the number of possible solutions of the coupled systems can be
reduced. The proposed method is robust and applicable in many different
systems.
