Spiral Attractors in a Reduced Mean-Field Model of Neuron-Glial Interaction

TL;DR

This paper analyzes a mean-field model of neuron-glial interactions, revealing how bifurcation scenarios like period doubling and chaos lead to various bursting activities in neural populations.

Contribution

It investigates bifurcation mechanisms in a phenomenological neuron-glial model, linking chaos and homoclinic attractors to bursting phenomena.

Findings

Bursting can emerge via period doubling bifurcations.

Chaos and homoclinic attractors are involved in bursting dynamics.

Multiple types of bursting activity are generated by spiral attractors.

Abstract

It is well known that bursting activity plays an important role in the processes of transmission of neural signals. In terms of population dynamics, macroscopic bursting can be described using a mean-field approach. Mean field theory provides a useful tool for analysis of collective behavior of a large populations of interacting units, allowing to reduce the description of corresponding dynamics to just a few equations. Recently a new phenomenological model was proposed that describes bursting population activity of a big group of excitatory neurons, taking into account short-term synaptic plasticity and the astrocytic modulation of the synaptic dynamics [1]. The purpose of the present study is to investigate various bifurcation scenarios of the appearance of bursting activity in the phenomenological model. We show that the birth of bursting population pattern can be connected both with the cascade of period doubling bifurcations and further development of chaos according to the Shilnikov scenario, which leads to the appearance of a homoclinic attractor containing a homoclinic loop of a saddle-focus equilibrium with the two-dimensional unstable invariant manifold. We also show that the homoclinic spiral attractors observed in the system under study generate several types of bursting activity with different properties.