With care, and keeping in mind that the biological plausibility of neuronal models with respect to the real brain activity is still an open question, we revisit some mathematical and numerical aspects of generalized Integrate and Fire (gIF) models and propose to eliminate assumptions related to spurious discontinuities. This concerns both the fire regime and then the integrate regime of the neuron. With this new point of view, some “biological ” results obtained on “models ” are to be reconsidered. This has also positive consequences. It allows us to reduce the bio-physical membrane equation to a very simple but powerful gIF numerical model. This also dramatically reduces the algorithmic complexity of event-based network simulations, as experimented here. 1

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