Fast global oscillations in networks of integrate-and-fire neurons with low firing rates

We study analytically the dynamics of a network of sparsely connected inhib itory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neuro ns N --> infinity, the network exhibits a sharp transition between a statio nary and an oscillatory global activity regime where neurons are weakly syn chronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that glob al oscillations of finite coherence time generically exist both above and b elow the critical inhibition threshold. Their characteristics are determine d as functions of systems parameters in these two different regimes. The re sults are found to be in good agreement with numerical simulations.