Synchrony in heterogeneous networks of spiking neurons

The emergence of synchrony in the activity of large, heterogeneous networks of spiking neurons is investigated. We define the robustness of synchrony by the critical disorder at which the asynchronous state becomes linearly u nstable. We show that at low firing rates, synchrony is more robust in exci tatory networks than in inhibitory networks, but excitatory networks cannot display any synchrony when the average firing rate becomes too high. We in troduce a new regime where all inputs, external and internal, are strong an d have opposite effects that cancel each other when averaged. In this regim e, the robustness of synchrony is strongly enhanced, and robust synchrony c an be achieved at a high firing rate in inhibitory networks. On the other h and, in excitatory networks, synchrony remains limited in frequency due to the intrinsic instability of strong recurrent excitation.