Role of synaptic delay in organizing the behavior of networks of self-inhibiting neurons

We consider a pair of mutually coupled inhibitory neurons in which each neuron is also self-inhibitory. We show that the size of the synaptic delay determines the existence and stability of solutions. For small delays, there is no synchronous solution, but a stable antiphase and a stable on-state solution. For long delays, only the synchronous solution is stable. For intermediate delays, either the antiphase or synchronous solutions are stable. In contrast to prior work, for stability of synchrony, we only require the existence of a single slow process.