Stability analysis of a single neuron model with delay

In this paper we study the asymptotic behavior and numerical approximation of the single neuron model equation ẋ(t)=−dx(t)+af(x(t))+bf(x(t−τ))+I, t⩾0 (1), where d>0 and f(x)=0.5(|x+1|−|x−1|). We obtain new sufficient conditions for global asymptotic stability of constant equilibriums of (1), give several numerical examples to illustrate our results, and formulate conjectures on the asymptotic behavior of the solutions based on our numerical experiments.