Three nested limit cycles in discontinuous piecewise linear differential systems with two zones
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Ponce, Enrique (E.T.S. Ingenieros(Sevilla))

Additional title:	Three limit cycles in discontinuous piecewise linear differential systems with two zones
Date:	2012
Abstract:	In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced by S. -M. Huan and X. -S. Yang in [8] who numerically showed that it can exhibit 3 limit cycles surrounding the real focus. This is the first example that a non-smooth piecewise linear differential system with two zones can have 3 limit cycles surrounding a unique equilibrium. We provide a rigorous proof of this numerical result.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 Ministerio de Ciencia e Innovación FEDER/MTM2008-03437
Note:	El títol de la versió pre-print de l'article és: Three limit cycles in discontinuous piecewise linear differential systems with two zones
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Non-smooth differential system ; Limit cycle ; Piecewise linear differential system
Published in:	Dynamics of continuous, discrete and impulsive systems, Vol. 19, Num. 3 (2012) , p. 325-335, ISSN 1918-2538

Postprint 8 p, 306.6 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles