Stochastic Resonance in Periodic Potentials Revisited

TL;DR

This paper demonstrates that stochastic resonance occurs in various periodic potentials, including bistable and washboard types, by analyzing hysteresis loop areas and signal-to-noise ratios, extending previous findings beyond sinusoidal potentials.

Contribution

It shows that stochastic resonance is not limited to sinusoidal potentials but also occurs in more general periodic bistable and washboard potentials, with a unified explanation based on dynamical states.

Findings

SR occurs in periodic bistable potentials.

SR is observed in washboard potentials after drift correction.

Hysteresis loop area peaks indicate SR in high-frequency drive regimes.

Abstract

The phenomenon of Stochastic Resonance (SR) has been conclusively demonstrated in bistable potentials. However, SR in sinusoidal potentials have only recently been shown numerically to occur in terms of hysteresis loop area. We show that the occurrence of SR is not specific to sinusoidal potentials and can occur in periodic bistable potential, $U(x)=2/3(\cos x +\cos 2x)$, as well. We further show that SR can occur even in a washboard potential, where hysteresis loops normally do not close because of average drift of particles. Upon correcting for the drift term, the closed hysteresis loop area (input energy loss) shows the usual SR peaking behaviour as also the signal-to-noise ratio in a limited domain in the high drive-frequency range. The occurrence of SR is attributed to the existence of effectively two dynamical states in the driven periodic sinusoidal and periodic bistable potentials. The same explanation holds also when the periodic potentials are tilted by a small constant slope.