  Stochastic integrate-and-fire (IF) neuron models have found widespread
applications in computational neuroscience. Here we present results on the
white-noise-driven perfect, leaky, and quadratic IF models, focusing on the
spectral statistics (power spectra, cross spectra, and coherence functions) in
different dynamical regimes (noise-induced and tonic firing regimes with low or
moderate noise). We make the models comparable by tuning parameters such that
the mean value and the coefficient of variation of the interspike interval
match for all of them. We find that, under these conditions, the power spectrum
under white-noise stimulation is often very similar while the response
characteristics, described by the cross spectrum between a fraction of the
input noise and the output spike train, can differ drastically. We also
investigate how the spike trains of two neurons of the same kind (e.g. two
leaky IF neurons) correlate if they share a common noise input. We show that,
depending on the dynamical regime, either two quadratic IF models or two leaky
IFs are more strongly correlated. Our results suggest that, when choosing among
simple IF models for network simulations, the details of the model have a
strong effect on correlation and regularity of the output.
