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

Abstract

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.

Dynamics in a Coupled FHN Model with Two Different Delays

“…The FHN model with cubic nonlinearity has been obtained from a simplified Hodgkin-Huxley(HH) neuron model [1][2][3]. Its complete topological and qualitative investigation has been carried out [4] and a rich variety of nonlinear phenomena such as hard oscillation, separatrix loops, bifurcations for equilibrium, resonance phenomena and limit cycles has been observed [5][6][7][8][9][10][11]. Since time delays always occur in the signal transmission for real neurons, Dhamala et al [12] made some theoretical discussion on coupled time-delay oscillators.…”