Average activity of excitatory and inhibitory neural populations

TL;DR

This paper extends the Ott-Antonsen method to analytically compute the mean activity of coupled excitatory and inhibitory neural populations, validating results with numerical simulations and comparing to Wilson-Cowan models.

Contribution

It introduces a novel extension of the Ott-Antonsen method for excitable units, enabling analytical study of mean neural activity in coupled populations.

Findings

Derived equations for order parameters of excitatory and inhibitory populations.

Observed compatible bifurcation diagrams with Wilson-Cowan models.

Identified higher-dimensional chaotic solutions in neural dynamics.

Abstract

We develop an extension of the Ott-Antonsen method that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared to those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible behaviors, as well as higher dimensional chaotic solutions, are observed. We study numerical simulations to further validate the equations.