  The stability of the dynamical states characterized by a uniform firing rate
({\it splay states}) is analyzed in a network of globally coupled leaky
integrate-and-fire neurons. This is done by reducing the set of differential
equations to a map that is investigated in the limit of large network size. We
show that the stability of the splay state depends crucially on the ratio
between the pulse--width and the inter-spike interval. More precisely, the
spectrum of Floquet exponents turns out to consist of three components: (i) one
that coincides with the predictions of the mean-field analysis [Abbott-van
Vreesvijk, 1993]; (ii) a component measuring the instability of
"finite-frequency" modes; (iii) a number of "isolated" eigenvalues that are
connected to the characteristics of the single pulse and may give rise to
strong instabilities (the Floquet exponent being proportional to the network
size). Finally, as a side result, we find that the splay state can be stable
even for inhibitory coupling.
