  We study the residence time distributions and explore the possibility of
observing stochastic resonance and synchonization of passages in a two-well
system driven by a periodic forcing of amplitude larger than a marginal value
beyond which one of the two wells become unstable and diasppear. We define and
calculate hysteresis loop in the system, the area of which measures the degree
of synchronization between the residence time statistics and the input signal,
as a function of input noise strength. We analyse the noise induced stability
obtained in such a deterministically overall unstable system and within this
context discuss the above two phenomena.
