Hopf bifurcation in a general n-neuron ring network with n time delays

In this paper, we consider a general ring network consisting of n neurons and n time delays. by analyzing the associated characteristic equation, a classification according to n is presented. it is investigated that hopf bifur-cation occurs when the sum of the n delays passes through a critical value.in fact, a family of periodic solutions bifurcate from the origin, while the zero solution loses its asymptotically stability. to illustrate our theoretical results, numerical simulation is given.