Chaotic oscillations in a map-based model of neural activity

TL;DR

This paper introduces a discrete map model for neural activity that exhibits chaotic oscillations, including spiking-bursting behavior, and explores various neural regimes through mathematical analysis.

Contribution

It presents a novel discontinuous two-dimensional map model capturing chaotic and other neural activity patterns, expanding understanding of neural dynamics.

Findings

The model exhibits chaotic attractors leading to chaotic spiking-bursting oscillations.

Various neural activity regimes such as subthreshold oscillations and phasic spiking are demonstrated.

Conditions for invariant regions and chaos in the model are identified.

Abstract

We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the phase plane, containing chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of other neural activities (subthreshold oscillations, phasic spiking etc.) derived from the proposed model.