Stochastic Resonance in a Bistable System with Multiplicative Square-wave Signal and Multiplicative Dichotomous Noise

Square-wave signal and dichotomous noise are widely used in scientific fields, and multiplicative signal is widely used in engineering practice. However, little study has been done on the nonlinear influence of multiplicative square-wave signal and multiplicative dichotomous noise on a bistable system, so in this paper we investigate the stochastic resonance phenomenon in a bistable system driven by multiplicative square-wave signal and multiplicative dichotomous noise is investigated. Under the adiabatic condition, the output signal-to-noise ratio (SNR) for the system is obtained. It is found that the SNR can obtain one maximum value and one minimum value with increasing the amplitude of the multiplicative square-wave signal and multiplicative dichotomous noise. Large values of the amplitude of the multiplicative square-wave signal can depress the system SNR, in the case of noise correlation rate λ=0.65, the system output amplitude for square-wave amplitude A=1.0 declines almost 29% by comparison with that for A=0.3, while a larger amount of the multiplicative dichotomous will improve the system output, in the case of system parameter b=3.8, the system output amplitude for multiplicative dichotomous noise intensity ε=3.5 is 2.5 times of that when ε=0.25. One resonance peak can be observed when the system SNR varies with the multiplicative white noise, with the additive white noise, as well as with the system parameters.