Canards from Chua's circuit

Jean-Marc Ginoux (1) , Jaume Llibre (2) , Leon L. O. Chua (3)

1 PROTEE - Processus de Transfert et d'Echanges dans l'Environnement - EA 3819
2 UAB - Departament de Matemàtiques [Barcelona]
3 Electronics Research Laboratory and Department of Electrical Engineering and Computer Sciences

The aim of this work is to extend Benoît'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.

Mots clés: Geometric singular perturbation method; flow curvature method; singularly perturbed dynamical systems; canard solutions

Domaines: Systèmes dynamiques [math.DS]

Jean-Marc Ginoux, Jaume Llibre, Leon L. O. Chua. Canards from Chua's circuit. International journal of bifurcation and chaos in applied sciences and engineering , 2013, 23 (4), pp.1330010. ⟨10.1142/S0218127413300103⟩. ⟨hal-01056966⟩