Resonance behaviour for a bistable system driven by random-phase square-wave signal-modulated noise and multiplicative noise

The stochastic resonance (SR) phenomenon for a bistable system subject to signal-modulated noise and to multiplicative and additive noise is investigated. The signal is modelled as a random-phase asymmetric square-wave one. Based on adiabatic approximation condition and two-state theory, the system output signal-to-noise ratio (SNR) is deduced. It is found that double SR phenomenon occurs when the SNR varies with the asymmetry of the square-wave signal. One resonance peak appears when the SNR changes with the amplitude of the square-wave signal. Traditional SR can be observed on the curves of the SNRs vs. the strength of the signal-modulated noise and vs. the intensities of the multiplicative and additive noise. The non-monotonous dependence of the SNR on the system parameter is discussed.