Dynamics of a discrete-time bidirectional ring of neurons with delay

This paper is devoted to the analysis of a discrete-time delayed Hopfield-type neural network of p ges 3 neurons with bidirectional ring architecture. The stability domain of the null solution is found, the values of the characteristic parameters for which bifurcations occur at the origin are identified and the existence of fold/cusp, Neimark-Sacker and higher codimension bifurcations is proved. The direction and stability of the Neimark-Sacker bifurcations are analyzed by applying the center manifold theorem and the normal form theory. Numerical simulations are given which substantiate the theoretical findings and suggest possible routes towards chaos when the absolute value of one of the characteristic parameters increases.