Canards from Chua's circuit

TL;DR

This paper extends Benoît's theorem to four-dimensional singularly perturbed systems, demonstrating the existence of canard solutions in Chua's circuit models using the Flow Curvature Method.

Contribution

It generalizes the theorem for higher dimensions and applies it to Chua's circuit, confirming canard solutions in these systems.

Findings

Canard solutions exist in four-dimensional Chua's models.

Flow Curvature Method effectively detects canards.

Extension of Benoît's theorem to higher dimensions.

Abstract

The aim of this work is to extend Beno\^it's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established that this result can be found according to the Flow Curvature Method. Applications to Chua's cubic model of dimension three and four enable to state the existence of "canards" solutions in such systems.