Existence and stability of a synchronous oscillation in a neural system with delayed coupling

The article deals with a particular case of a two-neuron network with two discrete time delays. We analyse the linear stability for the particular equilibrium ( 0 , 0 ) , and address the Hopf bifurcation which may occur as one of the delays crosses some critical values. The network under consideration has no self-connections, and thus only one time delay appears in the characteristic equation.