# Neural Activity of Heterogeneous Inhibitory Spiking Networks with Delay

## TL;DR

This paper investigates how inhibitory delays and heterogeneity influence neural network dynamics, revealing mechanisms for collective oscillations, neural inactivation, and reactivation in both dense and sparse spiking neuron networks.

## Contribution

It introduces a comprehensive analysis of inhibitory delayed pulses in heterogeneous spiking networks, highlighting new effects of delay and heterogeneity on collective behavior.

## Key findings

- Increased inhibition induces winner-takes-all firing suppression.
- Large delays lead to collective oscillations beyond a critical coupling.
- Heterogeneity promotes neural inactivation and asynchronous states.

## Abstract

We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner Takes All mechanism. For sufficiently large transmission delay we observe the emergence of collective oscillations in the system beyond a critical coupling value. Heterogeneity promotes neural inactivation and asynchronous dynamics and its effect can be counteracted by considering longer time delays. In sparse networks, inhibition has the counterintuitive effect of promoting neural reactivation of silent neurons for sufficiently large coupling. In this regime, current fluctuations are on one side responsible for neural firing of sub-threshold neurons and on the other side for their desynchronization. Therefore, collective oscillations are present only in a limited range of coupling values, which remains finite in the thermodynamic limit. Out of this range the dynamics is asynchronous and for very large inhibition neurons display a bursting behaviour alternating periods of silence with periods where they fire freely in absence of any inhibition.