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

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.