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We consider a fully stochastic excitatory neuronal network with a number ofsubpopulations with different firing rates. We show that as network size goesto infinity, this limits on a deterministic hybrid model whose trajectories arediscontinuous. The jumps in the limit correspond to large synchronous eventsthat involve a large proportion of the network. We also perform a rigorousanalysis of the limiting deterministic system in certain cases, and show thatit displays synchrony and periodicity in a large region of parameter space.

Synchrony and Periodicity in an Excitable Stochastic Neural Network with Multiple Subpopulations