This paper investigates a new asymmetric bistable model driven by correlated multiplicative colored noise and additive white noise. The mean first-passage time (MFPT) and the signal-to-noise ratio (SNR) as the indexes of evaluating the model are researched. Based on the two-state theory and the adiabatic approximation theory, the expressions of MFPT and SNR have been obtained for the asymmetric bistable system driven by a periodic signal, correlated multiplicative colored noise and additive noise. Simulation results show that it is easier to generate stochastic resonance (SR) to adjust the intensity of correlation strength [Formula: see text]. Meanwhile, the decrease of asymmetric coefficient [Formula: see text] and the increase of noise intensity are beneficial to realize the transition between the two steady states in the system. At the same time, the twice SR phenomena can be observed by adjusting additive white noise and correlation strength. The influence of asymmetry of potential function on the MFPTs in two different directions is different.
