Impact of heavy-tailed synaptic strength distributions on self-sustained activity in networks of spiking neurons

TL;DR

This paper investigates how heavy-tailed synaptic strength distributions influence self-sustained activity in spiking neuron networks, revealing conditions for bistability and percolation thresholds through analytical and theoretical methods.

Contribution

It provides analytical insights into the effects of heavy-tailed versus Gaussian synaptic distributions on network activity, including the existence of percolation thresholds and transition types.

Findings

Bistability between low and high activity states exists for both Gaussian and Cauchy couplings.

A directed percolation threshold is analytically derived for Cauchy coupling networks.

Transition nature (continuous or discontinuous) depends on excitatory-inhibitory balance.

Abstract

We analyze states of stationary activity in randomly coupled quadratic integrate-and-fire neurons using stochastic mean-field theory. Specifically, we consider the two cases of Gaussian random coupling and Cauchy random coupling, which are representative of systems with light- or with heavy-tailed synaptic strength distributions. For both, Gaussian and Cauchy coupling, bistability between a low activity and a high activity state of self-sustained firing is possible in excitable neurons. In the system with Cauchy coupling we find analytically a directed percolation threshold, i.e., above a critical value of the synaptic strength, activity percolates through the whole network starting from a few spiking units only. The existence of the directed percolation threshold is in agreement with previous numerical results in the literature for integrate-and-fire neurons with heavy-tailed synaptic strength distribution. However, we have found that the transition can be continuous or discontinuous, depending on the excitatory-inhibitory imbalance in the network. Networks with Gaussian coupling and networks with Cauchy coupling and additional additive noise lack the percolation transition in the thermodynamic limit.