Asymptotic Limit-cycle Analysis of the FitzHugh-Nagumo Equations

TL;DR

This paper provides an explicit analytical expression for the period of relaxation oscillations in the FitzHugh-Nagumo equations and identifies critical parameters for canard phenomena, enhancing understanding of neuronal dynamics.

Contribution

It introduces a precise analytical formula for oscillation periods and determines parameter thresholds for canard explosions and implosions in the FitzHugh-Nagumo model.

Findings

Analytical expression for oscillation period accurate within 1%

Critical parameters for canard explosions identified

Enhanced understanding of limit cycle behaviors

Abstract

The asymptotic limit-cycle analysis of the FitzHugh-Nagumo equations is presented. In this work, we obtain an explicit analytical expression for the relaxation-oscillation period that is accurate within 1\% of their numerical values. In addition, we derive the critical parametric values leading to canard explosions and implosions in its associated limit cycles.