Stability and Hopf bifurcation in an unidirectional ring of n neurons with distributed delays

In this paper we consider an unidirectional ring of n neurons with distributed delays. The effects of the delay, the coupling strengths and the network size on the stability of the system are investigated. Taking the average delay as a bifurcation parameter, we find two critical values depending on the network size and the coupling strengths, at which the system undergoes Hopf bifurcations. By using the method of multiple scales, we can show that these Hopf bifurcating periodic solutions are asymptotically stable. Finally, the theoretical results are illustrated by numerical simulations for the neural networks with three or four neurons.