Canards Existence in Memristor's Circuits

TL;DR

This paper introduces a new method to determine the existence of canard solutions in high-dimensional singularly perturbed systems, specifically applied to memristor-based chaotic circuits with smooth nonlinear characteristics.

Contribution

It proposes a unified, generic condition for canard existence in 3- and 4D systems, validated on memristor Chua's circuits with smooth nonlinearities.

Findings

Canard solutions exist in memristor Chua's circuits with smooth nonlinearities.

The method confirms the presence of canards in these circuits.

The approach aligns with previous theoretical conditions for canard existence.

Abstract

The aim of this work is to propose an alternative method for determining the condition of existence of "canard solutions" for three and four-dimensional singularly perturbed systems with only one fast variable in the folded saddle case. This method enables to state a unique generic condition for the existence of "canard solutions" for such three and four-dimensional singularly perturbed systems which is based on the stability of folded singularities of the normalized slow dynamics deduced from a well-known property of linear algebra. This unique generic condition is perfectly identical to that provided in previous works. Application of this method to the famous three and four-dimensional memristor canonical Chua's circuits for which the classical piecewise-linear characteristic curve has been replaced by a smooth cubic nonlinear function according to the least squares method enables to show the existence of "canard solutions" in such Memristor Based Chaotic Circuits.