Maximum number of limit cycles for certain piecewise linear dynamical systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Teixeira, Marco Antonio (Universidade Estadual de Campinas. Departamento de Matemática)

Data:	2015
Resum:	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.
Ajuts:	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.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Discontinuous differential system ; Limit cycles ; Piecewise linear differential system
Publicat a:	Nonlinear Dynamics, Vol. 82 Núm. 3 (2015) , p. 1159-1175, ISSN 1573-269X

DOI: 10.1007/s11071-015-2223-x

Postprint 26 p, 420.9 KB

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