Deterministic analysis of stochastic FHN systems based on Gaussian decoupling

This paper systematically explores the deterministic characteristics of FitzHugh-Nagumo (FHN) systems’ response to synaptic noise in statistical sense. With the help of Gauss decoupling approximation, two substitute systems of FHN systems’ response to synaptic noise are established by ignoring the cumulants higher than the second order, and the feasibilities of using the substitute systems for response analysis are demonstrated through error analysis. Then, the deterministic analyses of FHN systems with synaptic noise are carried out by means of the two substitute systems. Numerical results show that whether it is the neuronal system or the network system, the synaptic noise can effectively regulate its dynamics, and induce the mode transitions of discharge activity. Based on the class II excitability of FHN neurons, the system activity has a nonlinear dependence on the noise parameter and the other variables of interest. Particularly, the synaptic noise not only makes the neuronal system transition from low-level to high-level narrow-amplitude oscillation by competing with the input signal, but also contributes to the response or detection of this system to weak input signals. This study reveals the deterministic characteristics of FHN systems with synaptic noise, which can provide a reference for the large-scale analysis.