Residence times of a particle in both the wells of a double-well system,under the action of zero-mean Gaussian white noise and zero-averaged buttemporally asymmetric periodic forcings, are recorded in a numericalsimulation. The difference between the relative mean residence times in the twowells shows monotonic variation as a function of asymmetry in the periodicforcing and for a given asymmetry the difference becomes largest at an optimumvalue of the noise strength. Moreover, the passages from one well to the otherbecome less synchronous at small noise strength as the asymmetry parameter(defined below) differs from zero, but at relatively larger noise strengths thepassages become more synchronous with asymmetry in the field sweep. We proposethat asymmetric periodic forcing (with zero mean) could provide a simple butsensible physical model for unidirectional motion in a symmetric periodicsystem aided by a symmetric Gaussian white noise.
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