The Integrate and Fire model is a class of mean-field evolutionary equations which describes the activity
of a population of neurons via their membrane potential. The structure of this equation is shared by
many models of neural networks, and the investigation of its qualitative properties is still an open and
challenging question. In this presentation we illustrate de basic mechanism of the I&F model and the
idea behind Harris method [1]. Then, we apply this technique to the study of the asymptotic behaviour
of the linear I&F model, which presents a singular boundary condition. We prove the exponentially fast
convergence of its solutions to the unique stationary state in a L1-weighted norm [3] and we support the
result with some numerical simulations [2]. [editor's note : see references in PDF file]