  We consider a fully stochastic excitatory neuronal network with a number of
subpopulations with different firing rates. We show that as network size goes
to infinity, this limits on a deterministic hybrid model whose trajectories are
discontinuous. The jumps in the limit correspond to large synchronous events
that involve a large proportion of the network. We also perform a rigorous
analysis of the limiting deterministic system in certain cases, and show that
it displays synchrony and periodicity in a large region of parameter space.
