Vibrational and Stochastic Resonance in the FitzHugh-Nagumo Neural Model with Multiplicative and Additive Noise

The vibrational resonance and stochastic resonance phenomena in the FitzHugh-Nagumo (FHN) neural model, driven by a high-frequency (HF) signal and a low-frequency (LF) signal and by coupled multiplicative and additive noises, is investigated. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with the increasing intensities of the multiplicative and additive noise as well as with the increasing system parameters of the FHN model. The influence of the coupling strength between the multiplicative and additive noises on the SNR is discussed.