Asymptotic constancy and periodicity for a single neuron model with delay Original Research Article

We study the single neuron model equation View the MathML sourceẋ(t)=−dx(t)+af(x(t))+bf(x(t−1))+I, t>0t>0, where View the MathML sourced>0,b>0 and View the MathML sourcef(x)=12(|x+1|−|x−1|). We examine the asymptotic behaviour of the solutions and confirm that although most of them are convergent, there exists a periodic solution if d