Relation between stochastic resonance and synchronization of passages in a double-well system

We calculate, numerically, the residence times (and their distribution) of a Brownian particle in a two-well system under the action of a periodic, saw-tooth-type, external field. We define hysteresis in the system. The hysteresis loop area is shown to be a good measure of synchronization of passages from one well to the other. We establish a connection between this stochastic synchronization and stochastic resonance in the system.