Resonance phenomenon for an underdamped bistable system with additive dichotomous noise and multiplicative noise

Vibrational resonance (VR) and stochastic resonance for an underdamped bistable system driven by one high-frequency (HF) and one low-frequency (LF) periodic force with additive dichotomous noise, additive white noise and multiplicative white noise are investigated. The dynamical equation corresponding to the LF periodic force is obtained by decomposing the system output into one HF motion and one LF motion. Under the condition of weak LF signal, based on two-state theory, the system output signal-to-noise ratio (SNR) is derived. It is shown that the SNR can reach one peak value with the variation of the amplitude of the dichotomous noise. VR phenomenon can be observed when the SNR varies with both the amplitude and the frequency of the HF signal. One resonance peak occurs when the SNR changes with the strength of the multiplicative noise. The SNR can obtain one maximum value as increasing the system damping coefficient and increasing the intensity of the additive noise.