| Integrate-and-fire (IF) neurons have found wide-spread applications in computational neuroscience, in particular, in stochastic versions of these models. Here we present results on the white-noise driven perfect, leaky, and quadratic integrate-and-fire models and focus on the spectral statistics (power spectra, cross spectra, and coherence functions) in different dynamical regimes (noise-induced and deterministic 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 agree for all of them. We find that under these conditions, the power spectrum under white-noise stimulation is very similar while the response characteristics (characterized by the cross spectrum between a fraction of the input noise and the output spike train) differs in part drastically. We also investigate how two neurons of the same kind (e.g. two leaky integrate-and-fire neurons) synchronize if they share a common noisy input. We show that depending on the dynamical regime either two quadratic IF models or two LIFs are best synchronized. Our results suggest that for network simulations when choosing among simple integrate-and-fire models, the details of the model have a strong effect on synchronization behavior and regularity of the output. |
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