Response to a periodic stimulus in a perfect integrate-and-fire neuron model driven by colored noise

The output interspike interval statistics of a stochastic perfect integrate-and-fire neuron model driven by an additive exogenous periodic stimulus is considered. The effect of temporally correlated random activity of synaptic inputs is modeled by an additive symmetric dichotomous noise. Using a first-passage-time formulation, exact expressions for the output interspike interval density and for the serial correlation coefficient are derived in the nonsteady regime, and their dependence on input parameters (e.g., the noise correlation time and amplitude as well as the frequency of an input current) is analyzed. It is shown that an interplay of a periodic forcing and colored noise can cause a variety of nonequilibrium cooperation effects, such as sign reversals of the interspike interval correlations versus noise-switching rate as well as versus the frequency of periodic forcing, a power-law-like decay of oscillations of the serial correlation coefficients in the long-lag limit, amplification of the output signal modulation in the instantaneous firing rate of the neural response, etc. The features of spike statistics in the limits of slow and fast noises are also discussed.