Stability analysis of the Hindmarsh-Rose neuron under electromagnetic induction

TL;DR

This paper investigates how electromagnetic induction influences the stability and dynamics of the Hindmarsh-Rose neuron model, showing that magnetic flux can stabilize fixed points and suppress chaotic or oscillatory behavior.

Contribution

It introduces a modified Hindmarsh-Rose model incorporating electromagnetic induction and analyzes how magnetic flux affects neuron stability and firing patterns.

Findings

Increasing magnetic flux stabilizes fixed points.

Electromagnetic induction reduces chaotic regimes.

Magnetic flux can suppress oscillations.

Abstract

We consider the Hindmarsh-Rose neuron model modified by taking into account the effect of electromagnetic induction on membrane potential. We study the impact of the magnetic flux on the neuron dynamics, through the analysis of the stability of fixed points. Increasing magnetic flux reduces the number of equilibrium points and favors their stability. Therefore, electromagnetic induction tends to regularize chaotic regimes and to affect regular and quasi-regular ones by reducing the number of spikes or even destroying the oscillations.