Stochastic resonance in a random walk

I demonstrate stochastic resonance in a discrete-state, continuous-time random walk in one dimension. The probabilities for the walker to step to the right or to the left depend on an external field. The field varies in space and time such that the walker feels a bistable, periodically modulated random potential. Unbiased random forces act on the walker in addition to the field. When the field is strong relative to the unbiased forces, the walker is confined to a single well, and a power spectrum shows low noise levels and little power at the modulation frequency. When the field is weak relative to the unbiased forces, the walker moves erratically between the wells, and a power spectrum is noisy. For intermediate field strengths, the walker moves periodically from one well to another, and the power at the modulation frequency increases dramatically with respect to the noise level. In this respect, the behavior of the discrete-state model is analogous to the standard, continuous-state Langevin models.