Stochastic modeling of the firing activity of coupled neurons periodically driven

A stochastic model for describing the firing activity of a couple of interacting\udneurons subject to time-dependent stimuli is proposed. Two stochastic differential equations suitably coupled and including periodic terms to represent stimuli imposed to one\udor both neurons are considered to describe the problem. We investigate the first passage\udtime densities through specified firing thresholds for the involved time non-homogeneous\udGauss-Markov processes. We provide simulation results and numerical approximations\udof the firing densities. Asymptotic behaviors of the first passage times are also given