  For large fully connected neuron networks, we study the dynamics of
homogenous assemblies of interacting neurons described by time elapsed models.
Under general assumptions on the firing rate which include the ones made in
previous works [7, 8, 6], we establish accurate estimate on the long time
behavior of the solutions in the weak and the strong connectivity regime both
in the case with and without delay. Our results improve [7, 8] where a less
accurate estimate was established and [6] where only smooth firing rates were
considered. Our approach combines several arguments introduced in the above
previous works as well as a slightly refined version of the Weyl's and spectral
mapping theorems presented in [13, 4].
