Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems witha a straight line of separation

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 s...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Torregrosa, Joan|||0000-0002-2753-1827, Teixeira, Marco Antonio|||0000-0002-5386-9282
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150641
Acceso en línea:https://ddd.uab.cat/record/150641
https://dx.doi.org/urn:doi:10.1142/S0218127413500661
Access Level:acceso abierto
Palabra clave:Non-smooth differential system
Limit cycle
Piecewise linear differential system
Descripción
Sumario: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.