A New Quantity to Characterize Stochastic Resonance

In a double-well system, we investigate theoretically the population distribution of a particle perturbed by a weak sinusoidal signal with a Gaussian white noise accompanied. Our numerical simulation shows that the probability of the particle staying in the right potential well, P_R, exhibits an extreme value at specific noise intensity D depending on the frequency of the sinusoidal signal, which is a key feature of stochastic resonance. This is confirmed by calculating the power spectrum of the output signal, in which the extreme value of the amplitude locates at the same noise intensity. These results provide us with a new way to quantify the stochastic resonance by measuring the population distribution of the particle.