Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons

TL;DR

This paper investigates how collective oscillations emerge and are destroyed in large networks of coupled type 1 neurons with two populations, revealing bifurcation scenarios and bistability relevant to neural functions.

Contribution

It provides a detailed bifurcation analysis of collective oscillations in two-population neuron networks with nonuniform coupling, highlighting mechanisms of their birth and destruction.

Findings

Oscillations arise with pulse width and are quenched otherwise.

Bifurcation scenarios organize oscillation dynamics.

Bistability enables switching between activity states.

Abstract

We study the macroscopic dynamics of large networks of excitable type 1 neurons composed of two populations interacting with disparate but symmetric intra- and inter-population coupling strengths. This nonuniform coupling scheme facilitates symmetric equilibria, where both populations display identical firing activity, characterized by either quiescent or spiking behavior, or asymmetric equilibria, where the firing activity of one population exhibits quiescent but the other exhibits spiking behavior. Oscillations in the firing rate are possible if neurons emit pulses with non-zero width but are otherwise quenched. Here, we explore how collective oscillations emerge for two statistically identical neuron populations in the limit of an infinite number of neurons. A detailed analysis reveals how collective oscillations are born and destroyed in various bifurcation scenarios and how they are organized around higher codimension bifurcation points. Since both symmetric and asymmetric equilibria display bistable behavior, a large configuration space with steady and oscillatory behavior is available. Switching between configurations of neural activity is relevant in functional processes such as working memory and the onset of collective oscillations in motor control.