Stochastic resonance in a sinusoidal potential system: An analog simulation experiment

Abstract

We setup an analog simulation experiment to verify the occurrence of stochastic resonance in an underdamped sinusoidal potential system driven by a periodic force and a Gaussian white noise. Stochastic resonance in such systems was numerically obtained recently and its occurrence in the system was explained in terms of two coexisting dynamical states having different amplitude and phase lag. At zero temperature these two initial condition-dependent dynamical states are stable. However, at elevated temperatures, these two states make transitions from one to the other at a mean rate. In the present experiment, we show the existence of these two dynamical states which contribute differently to the hysteresis loss. In order to verify the occurrence of stochastic resonance we use the mean hysteresis loss as a quantifier. The mean hysteresis loss depends on the fraction of the two dynamical states at any temperature. Hence, we are necessarily required to set the initial conditions of the experiment appropriately. We explain the procedure to set the initial conditions in the experiment.