Computational of periodic oscillations and related bifurcations in the Hodgkin-Huxley model

TL;DR

This paper applies the harmonic balance method to detect and analyze periodic oscillations and bifurcations in the Hodgkin-Huxley neuronal model, enhancing understanding of its dynamic behavior.

Contribution

It introduces a robust harmonic balance approach to identify and characterize periodic solutions and bifurcations in the Hodgkin-Huxley model.

Findings

Successfully detects stable and unstable periodic solutions

Provides detailed bifurcation analysis of the model

Enhances computational methods for neuronal dynamics

Abstract

The Hodgkin-Huxley equations constitute one of the more realistic neuronal models in literature and the most accepted one. It is well known that, depending on the value of the external stimuli current, it exhibits periodic solutions, both stable and unstable. Our aim is to detect and characterize such periodic solutions, exploiting a robust and manageable technique, mainly based on harmonic balance method