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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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Discontinuous differential system ; Limit cycles ; Piecewise linear differential system
Publicat a: Nonlinear Dynamics. An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, Vol. 82 Núm. 3 (2015) , p. 1159-1175, ISSN 1573-269X

DOI: 10.1007/s11071-015-2223-x

26 p, 420.9 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Articles > Articles de recerca
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 Registre creat el 2016-01-12, darrera modificació el 2017-01-13

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