- A model of many heterogeneous excitable neurons with a global slowly decaying inhibitory coupling is studied. When neuronal intrinsic excitability parameters are randomly distributed, the system exhibits four regimes of behavior. In addition to synchronized periodic and asynchronous regimes, we obtain two aperiodic regimes, with bursting rate a staircaselike function of neuron excitability. In one regime, the system is partially synchronized and in the second, partially antisynchronized. The transition between these two regimes is discontinuous as the disorder increases.