Stochastic resonance in a mono-stable system subject to frequency mixing periodic force and noise

The phenomenon of stochastic resonance (SR) in a biased mono-stable system driven by multiplicative and additive white noise and two periodic fields is investigated. Analytic expressions of the signal-to-noise ratio (SNR) for fundamental harmonics and higher harmonics are derived by using the two-state theory. It is shown that the SNR is a non-monotonic function of the intensities of the multiplicative and additive noises, as well as the bias of the mono-stable system and SR appears at both fundamental harmonics and higher harmonics. Moreover, the higher the order of mixed harmonics is, the smaller the SNR values are, that is, the suppression exists for higher harmonics.