Bifurcation Analysis of the Driven FitzHugh-Nagumo Oscillator: Prediction and Experiment

TL;DR

This paper presents a comprehensive bifurcation analysis of the driven FitzHugh-Nagumo oscillator, combining numerical regime maps with experimental circuit measurements to understand oscillatory behaviors, including chaos and subharmonic cycles.

Contribution

It provides the first detailed, experimentally validated bifurcation map of the driven FitzHugh-Nagumo oscillator, extending previous partial maps and enhancing understanding of its complex dynamics.

Findings

Numerical and experimental maps show good agreement.

Identified an island of unstable oscillations with subharmonic and chaotic behavior.

Extended previous bifurcation maps with a more detailed regime map.

Abstract

Bifurcation analysis is applied to the FitzHugh-Nagumo oscillator driven by a sinusoidal source. A numerically generated 2d regime map showing the variety of oscillatory dynamics in the parameter space of source frequency and amplitude agrees well with a map created from analog circuit measurements. Application of the sinusoidal source to the fast variable's first-order differential equation produces an island in the map in which oscillations at the source frequency are unstable and the behavior is dominated by two distinct families of subharmonic limit cycles and by chaos. Previously published maps are portions of the map shown here and are shown to be consistent with it. The more detailed and comprehensive regime map presented here should facilitate the understanding of this foundational system and thereby aid the ongoing research involving more complicated implementations of the Fitzhugh-Nagumo system.