  The activity of a sparse network of leaky integrate-and-fire neurons is
carefully revisited with reference to a regime of a bona-fide asynchronous
dynamics. The study is preceded by a finite-size scaling analysis, carried out
to identify a setup where collective synchronization is negligible. The
comparison between quenched and annealed networks reveals the emergence of
substantial differences when the coupling strength is increased, via a scenario
somehow reminiscent of a phase transition. For sufficiently strong synaptic
coupling, quenched networks exhibit a highly bursting neural activity, well
reproduced by a self-consistent approach, based on the assumption that the
input synaptic current is the superposition of independent renewal processes.
The distribution of interspike intervals turns out to be relatively
long-tailed; a crucial feature required for the self-sustainment of the
bursting activity in a regime where neurons operate on average (much) below
threshold. A semi-quantitative analogy with Ornstein-Uhlenbeck processes helps
validating this interpretation. Finally, an alternative explanation in terms of
Poisson processes is offered under the additional assumption of mutual
correlations among excitatory and inhibitory spikes.

Neurons and Cognition;Adaptation and Self-Organizing Systems