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 x(t)=-dx(t)+af(x(t))+bf(x(t-tau))+I, t greater than or equal to 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. (C) 2003 Elsevier B.V. All rights reserved.