We analyze a stochastic neuronal network model which corresponds to an all-to-all network
of discretized integrate-and-fire neurons where the synapses are failure-prone. This
network exhibits different phases of behavior corresponding to synchrony and asynchrony,
and we show that this is due to the limiting mean-field system possessing multiple
attractors. We also show that this mean-field limit exhibits a first-order phase
transition as a function of the connection strength — as the synapses are made more
reliable, there is a sudden onset of synchronous behavior. A detailed understanding of the
dynamics involves both a characterization of the size of the giant component in a certain
random graph process, and control of the pathwise dynamics of the system by obtaining
exponential bounds for the probabilities of events far from the mean.