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

Edward H. Hellen

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arXiv · 2512.04212

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

Edward H. Hellen

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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.

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Edward H. Hellen. 2025-12-03. Bifurcation Analysis of the Driven FitzHugh-Nagumo Oscillator: Prediction and Experiment. https://arxiv.org/abs/2512.04212

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