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Maximum number of limit cycles for certain piecewise linear dynamical systems
Llibre, Jaume
Novaes, Douglas D.
Teixeira, Marco Antonio

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

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)
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 Registre creat el 2016-01-12, darrera modificació el 2016-06-04

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