Canards Existence in Memristor's Circuits

Jean-Marc Ginoux (1) , Jaume Llibre (2)

1 PROTEE - Processus de Transfert et d'Echanges dans l'Environnement - EA 3819
2 UAB - Departament de Matemàtiques [Barcelona]

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four-dimensional memristor canonical Chua's circuits for which the classical piecewise-linear characteristic curve has been replaced by a smooth cubic nonlinear function according to the least squares method enables to show the existence of " canard solutions " in such Memristor Based Chaotic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.

Mots clés: Geometric singular perturbation theory; singularly perturbed dy- namical systems; canard solutions

Domaines: Systèmes dynamiques [math.DS]; Electronique

Jean-Marc Ginoux, Jaume Llibre. Canards Existence in Memristor's Circuits. Qualitative Theory of Dynamical Systems, 2016, 15 (2), pp.383 - 431. ⟨10.1007/s12346-015-0160-1⟩. ⟨hal-01856950⟩