Periodically time-modulated bistable systems: Nonstationary statistical properties

Abstract

The relaxation properties of a one-dimensional overdamped system modulated by an external periodic force are studied analytically by means of a perturbation approach. The validity of the approximations introduced is discussed in detail. The nonstationary nature of the process is illustrated by evaluating explicitly the autocorrelation function for the relaxation in a bistable potential. The predictions thus obtained are shown to compare favorably with the results of analogue simulation for the case of a quartic double-well potential. The stochastic resonance mechanism is proven to set in only when the periodic perturbation breaks the symmetry of the bistable potential.