  In order to describe the firing activity of a homogenous assembly of neurons,
we consider time elapsed models, which give mathematical descriptions of the
probability density of neurons structured by the distribution of times elapsed
since the last discharge. Under general assumption on the firing rate and the
delay distribution, we prove the uniqueness of the steady state and its
nonlinear exponential stability in the weak connectivity regime. The result
generalizes some similar results obtained in [10] in the case without delay.
Our approach uses the spectral analysis theory for semigroups in Banach spaces
developed recently by the first author and collaborators.
