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Página principal > Artículos > Artículos publicados > Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems witha a straight line of separation |
Título variante: | On the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation |
Fecha: | 2013 |
Resumen: | 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. |
Ayudas: | Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
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. |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Non-smooth differential system ; Limit cycle ; Piecewise linear differential system |
Publicado en: | International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 4 (2013) , p. 1350066 (10 pages), ISSN 1793-6551 |
Postprint 14 p, 377.1 KB |