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 inhibitory integrate-and-re neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N ! 1, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. 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 nite networks, the analysis shows that global oscillations of nite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters, in these two dierent regimes. The results are found to be in good agreement with numerical simulations. Neural Computation, 11, 1621-1671 (1999) 1..