Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise

Stochastic resonance in an underdamped bistable system subjected to a weak asymmetric dichotomous noise is investigated numerically. Dichotomous noise is a non-Gaussian color noise and more complex than Gaussian white noise, whose waiting time complies with the exponential distribution. Utilizing an efficiently numerical algorithm, we acquire the asymmetric dichotomous noise accurately. Then the system responses and the averaged power spectrum as the signatures of the stochastic resonance are calculated by the fourth-order Runge-Kutta algorithm. The effects of the noise strength, the forcing frequency, and the asymmetry of dichotomous noise on the system responses and the effects of the forcing frequency on the averaged power spectrum are discussed, respectively. It is found that the increasing of the noise strength or the forcing frequency could strengthen the passage between the stable points of the system, and the system responses also display the asymmetry for the asymmetric dichotomous noise, which has not been discovered in other investigated results. Additionally, the averaged power spectrum exhibits the sharp peaks, which indicates the occurrence of stochastic resonance, and we also discover two critical forcing frequencies: one denoting the transformation of the peaks and another for the optimum on stochastic resonance.