Activity patterns in ring networks of quadratic integrate-and-fire neurons with synaptic and gap junction coupling

TL;DR

This paper investigates activity patterns in a ring network of quadratic integrate-and-fire neurons with synaptic and gap junction coupling, analyzing wave solutions and their bifurcations through a neural field model.

Contribution

It introduces a neural field model that captures complex wave solutions in quadratic integrate-and-fire neuron networks with nonlocal coupling, and performs bifurcation analysis on gap junction effects.

Findings

Existence of standing, traveling, and lurching waves in the network.

Self-consistency equations effectively track solution changes with parameters.

Bifurcation analysis reveals how gap junction strength influences wave dynamics.

Abstract

We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and travelling waves, and also lurching waves. We show that many of these solutions satisfy self-consistency equations which can be used to follow them as parameters are varied. We perform numerical bifurcation analysis of the neural field model, concentrating on the effects of varying gap junction coupling strength. Our methods are generally applicable to a wide variety of networks of quadratic integrate-and-fire neurons.