Canards from Chua's circuit
Ginoux, Jean-Marc (Université du Sud(France). Laboratoire Protee)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Chua, Leon O. (University of California. DEECS Department)

Date:	2013
Abstract:	At first, 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 enables to state existence of "canards" solutions in such systems.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338
Note:	Agraïments: First author would like to thank Prof. Martin Wechselberger for his fruitful advices. Moreover, let's notice that our main result has been already established by Wechselberger [2012] who has extended canard theory of singularly perturbed systems to the more general case of k + m-dimensional singularly perturbed systems with k slow and m fast dimensions, with k > 2 and m > 1.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Geometric singular perturbation method ; Flow curvature method ; Singularly perturbed dynamical systems ; Canard solutions
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 4 (2013) , p. 1330010, ISSN 1793-6551

DOI: 10.1142/S0218127413300103

Postprint 21 p, 917.4 KB

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