Canards Existence in Memristor's Circuits
Ginoux, Jean-Marc (Université de Toulon(France). Laboratoire LSIS)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
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four-dimensional memristor canonical Chua's circuits for which the classical piecewise-linear characteristic curve has been replaced by a smooth cubic nonlinear function according to the least squares method enables to show the existence of "canard solutions" in such Memristor Based Chaotic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.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Ciencia e Innovación MTM2009-03437 Ministerio de Ciencia e Innovación MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 316339
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Canard solutions ; Geometric singular perturbation theory ; Singularly perturbed dynamical systems
Published in:	Qualitative theory of dynamical systems, 2016 , ISSN 1662-3592

DOI: 10.1007/s12346-015-0160-1

Postprint 46 p, 1.1 MB

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