On the Dynamics of a Couple of Mutually Interacting Neurons

A model for describing the dynamics of two mutually interacting neurons is considered. In such a context, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point of the membrane potential of one of the two neurons when a spike of the other one occurs. We give an approximation for the interspike time interval probability density function of both neurons within any parametric configurations driving the evolution of the membrane potentials in the so-called subthreshold regimen.