This paper presents pulse-coupled two bifurcating neurons. The single neuron is represented by a spike position map and the coupled neurons can be represented by a composition of the spike position maps. Using the composite map, we can analyze basic bifurcation phenomena and can find some interesting phenomena that are caused by the pulse-coupling and are impossible in the single neuron. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

This article theoretically provides the ensemble average and the ensemble variance of membrane potential of an integrate-and-fire neuron, when the neuron receives random spikes from the other neurons. The model assumes that EPSPs rise and fall continuously. Our theoretical result shows good agreement with a numerical simulation.