Synchrony and Periodicity in Excitable Neural Networks with Multiple Subpopulations

We consider a cascading model of excitable neural dynamics and show that over a wide variety of parameter regimes, these systems admit unique attractors. For large coupling strengths, this attractor is a limit cycle, and for small coupling strengths, it is a fixed point. We also show that the cascading model considered here is a mean-field limit of an existing stochastic model.