Interspike interval distribution of a resonate-and-fire neuron model driven by Mittag-Leffler noise

Abstract

Based on the dynamics of a generalized Langevin equation subjected to a power-law-type memory kernel with a finite memory time a resonate-and-fire neuron model is considered. The effect of temporally correlated random neuronal input is modeled as a Mittag-Leffler noise. Using a first-passage-time formulation, the exact expression for the output interspike interval density is derived and its dependence on input parameters, especially on the memory time and on the memory exponent, is analyzed. Particularly, in the case of external white noise it is shown that at intermediate values of the memory exponent the survival probability (the probability that spikes are not generated) is significantly enhanced in comparison with the cases of strong and weak memory, which causes a resonance-like suppression of the interspike interval distribution versus the memory exponent. Similarities and differences between the behaviors of the models at internal and external noises are also discussed.