Slow dynamics of neuronal excitability under pulse stimulation

TL;DR

This paper investigates the long-term firing behavior of neurons under pulse stimulation, showing that common models exhibit stable, periodic patterns rather than chaos, and introduces a new analytical approach.

Contribution

It introduces a piecewise linear map to analyze neuronal dynamics, demonstrating that typical models do not display chaos but only stable periodic firing.

Findings

Neuronal models studied are not chaotic under pulse stimulation.

Neuronal firing patterns are stable and periodic, not irregular or chaotic.

A new analytical method simplifies understanding long-term neuronal dynamics.

Abstract

Neurons fire irregularly on multiple timescales when stimulated with a periodic pulse train. This raises two questions: Does this irregularity imply significant intrinsic stochasticity? Can existing neuron models be readily extended to describe behavior at long timescales? We show here that for commonly studied neuronal models, dynamics is not chaotic and can only produce stable and periodic firing patterns. This is done by transforming the neuron model to an analytically tractable piecewise linear discrete map. Thus we answer "yes" and "no" to the above questions, respectively.