A new technique is used to reduce the classic Hodgkin-Huxley model to a two-dimensional neuronal model which retains the essential features of the full description. The resulting equations are similar in spirit to those of the FitzHugh-Nagumo model, but they exhibit some essential diierences which provide a more accurate representation of the full dynamics. By further simplifying the two-dimens...

This thesis considers a stochastic dynamical system that has multiple time scales. The focus lies on the planar slow-fast stochastic differential equation (a singularly perturbed stochastic system) modeling the spiking activity of an isolated FitzHugh-Nagumo neural oscillator. We analyze the model equation on the slow time scale τ (Eq.(1)) and on the fast time scale t (Eq.(2)). { dvτ = ε f(vτ ,...

<p style='text-indent:20px;'>We investigate the formation of stationary patterns in FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on effects Turing mechanism. Linear stability indicates that positive values inhibitor enlarge region parameter space where a instability is excited. A sufficiently large coefficient removes requirement impos...