Per citar aquest document: http://ddd.uab.cat/record/150641
Scopus: 18 cites, Web of Science: 10 cites,
Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems witha a straight line of separation
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Títol variant: On the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation
Data: 2013
Resum: In this paper we study the maximum number of limit cycles for planar discontinuous piecewise linear differential systems defined in two half–planes separated by a straight line. Here we only consider non-sliding limit cycles. For that systems, the interior of any limit cycle only contains a unique singular point or a unique sliding segment. Moreover, the linear differential systems that we consider in every half–plane can have either a focus (F), or a node (N), or a saddle (S), these equilibrium points can be real or virtual. Then, we can consider six kinds of planar discontinuous piecewise linear differential systems: FF, FN, FS, NN, NS, SS. We analyze for each of these types of discontinuous differential systems the maximum number of known limit cycles.
Nota: El títol de la versió pre-print de l'article és: On the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation
Nota: Agraïments: The second author is partially supported by the FAPESP-BRAZIL grant 2007/06896-5. All the authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC.
Nota: Número d'acord de subvenció MICINN/MTM2008-03437
Nota: Número d'acord de subvenció AGAUR/2009/SGR-410
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Non–smooth differential system ; Limit cycle ; Piecewise linear differential system
Publicat a: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 23 Núm. 4 (2013) , p. 1350066 (10 pages), ISSN 1793-6551

DOI: 10.1142/S0218127413500661


Preprint
14 p, 377.1 KB

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