Some stochastic phenomena in a driven double-well system

We study the overdamped motion of a Brownian particle in a driven double-well system to understand various physical phenomena observed experimentally. These phenomena include hysteresis, stochastic resonance, and net undirectional motion in a symmetric periodic system. We argue that the area of the hysteresis loop so defined is a good measure of synchronization (with respect to the applied field) of passages between the two wells. We find that stochastic resonance may be relevant even in case of large-amplitude driving field due to a recently discovered phenomena of noise-induced stability of unstable states. We try to find the relation between some of these apparently different phenomena.