Periodic solutions in an inhibitory two-neuron network

In this paper, we consider a delayed network of two neurons with self-feedback and interaction described by an all-or-none threshold function. The discontinuity of signal function makes it difficult to apply directly dynamical system. We show that the dynamics of the network can be understood in terms of the iterations of a one-dimensional map, and we obtain the existence and attractivity of periodic solutions. Moreover, because the network is a limiting case of the corresponding smooth system as the parameter tends to infinity, the above results can act as the guide to the rich dynamics of the smooth system. Therefore, our results have important significance in both theory and applications.