Resonance in a Stochastic Neuron Model with Delayed Interaction

We study here a simple stochastic single neuron model with delayed self-feedback capable of generating spike trains. In order to gain insight into this resonance, we simplify the model and study a stochastic binary element whose transition probability depends on its state at a fixed interval in the past. With this simplified model we can analytically compute interspike interval histograms, and show how the resonance between noise and delay arises. The resonance is also observed when such elements are coupled through delayed interaction.