  Ensembles of phase-oscillators are known to exhibit a variety of collective
regimes. Here, we show that a simple mean-field model involving two
heterogenous populations of pulse-coupled oscillators, exhibits, in the
strong-coupling limit, a robust irregular macroscopic dynamics. The resulting,
strongly synchronized, regime is sustained by a homeostatic mechanism induced
by the shape of the phase-response curve combined with adaptive coupling
strength, included to account for energy dissipated by the pulse emission. The
proposed setup mimicks a neural network composed of excitatory and inhibitory
neurons.
