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

TL;DR

This paper analytically investigates the emergence of global oscillations in large networks of inhibitory integrate-and-fire neurons with low firing rates, revealing the conditions for oscillation onset and properties.

Contribution

It provides a theoretical analysis of oscillation dynamics in inhibitory neuron networks, highlighting the role of synaptic times and external input in oscillation characteristics.

Findings

Global oscillations occur when inhibitory feedback is strong enough.

Oscillation period mainly depends on synaptic times.

Finite networks exhibit oscillations with finite coherence time.

Abstract

We study analytically the dynamics of a network of sparsely connected inhibitory 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 neurons N tends to infinity,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 finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters, in these two different regimes. The results are found to be in good agreement with numerical simulations.