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Página principal > Artículos > Artículos publicados > Maximum number of limit cycles for certain piecewise linear dynamical systems |
Fecha: | 2015 |
Resumen: | This paper deals with the question of the determinacy of the maximum number of limit cycles of some classes of planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line \Sigma. We restrict ourselves to the non-sliding limit cycles case, i. e. , limit cycles that do not contain any sliding segment. Among all cases treated here, it is proved that the maximum number of limit cycles is at most 2 if one of the two linear differential systems of the discontinuous piecewise linear differential system has a focus in \Sigma, a center, or a weak saddle. We use the theory of Chebyshev systems for establishing sharp upper bounds for the number of limit cycles. Some normal forms are also provided for these systems. |
Ayudas: | Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 |
Nota: | Agraïments: The second author was partially supported by a FAPESP Grant 2012/10231-7. The third authors was partially supported by a FAPESP Grant 2012/18780-0. The three authors are also supported by a CAPES CSF-PVE Grant 88881.030454/2013-01 from the program CSF-PVE. |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Discontinuous differential system ; Limit cycles ; Piecewise linear differential system |
Publicado en: | Nonlinear Dynamics, Vol. 82 Núm. 3 (2015) , p. 1159-1175, ISSN 1573-269X |
Postprint 26 p, 420.9 KB |