Chaotic Dynamics and Bifurcation Analysis of the Hindmarsh-Rose Neuron Model with Blue-Sky Catastrophe under Magnetic Field Influence

TL;DR

This study explores how magnetic fields influence the chaotic and bifurcation behavior of the Hindmarsh-Rose neuron model, revealing electromagnetic feedback as a means to control neuronal dynamics and chaos.

Contribution

It introduces a magnetic flux variable into the model, demonstrating how electromagnetic effects can modulate bifurcation structures and neuronal firing patterns in novel ways.

Findings

Weak magnetic coupling preserves regular spiking and bursting

Intermediate coupling induces chaotic bursting

Strong coupling leads to irregular but structured dynamics

Abstract

We investigate the impact of magnetic-field-induced feedback on the dynamics of a Hindmarsh-Rose neuron model exhibiting a blue-sky catastrophe. By introducing a magnetic flux variable that couples nonlinearly to the membrane potential, we demonstrate that electromagnetic effects profoundly reshape neuronal firing patterns and bifurcation structure. Interspike-interval bifurcation analysis reveals a nonmonotonic dependence on the magnetic coupling strength, with weak coupling preserving regular spiking and bursting, intermediate coupling promoting chaotic bursting, and strong coupling yielding structured irregular dynamics. These transitions are quantitatively characterized using the largest Lyapunov exponent computed via the Wolf algorithm and supported by Poincar\'e sections and time-series analysis. Our results establish electromagnetic feedback as a robust and tunable mechanism for controlling instability and chaos in slow-fast neuronal systems.