Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays

In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, fold or Neimark-Sacker bifurcations occur, but codimension 2 (fold-NeimarkSacker, double Neimark Sacker and resonance 1:1) bifurcations may also be present. The direction and the stability of the Neimark-Sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory.