Hopf bifurcation analysis for a two-neuron network with four delays

A delay-differential system modelling an artificial neural network with two neurons is investigated. At appropriate parameter values, linear stability and Hopf bifurcation including its direction and stability of the network with four delays are established in this paper. The main tools to obtain our results are the normal form method and the center manifold theory introduced by Hassard. Simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. Our results extend and complement some earlier publications.