Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line

In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain aga...

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Detalles Bibliográficos
Autores: Bastos, J.L.R., Buzzi, C.A., Torregrosa, J.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/536854
Acceso en línea:http://hdl.handle.net/2072/536854
Access Level:acceso abierto
Palabra clave:Center-focus problem
Local cyclicity
Nonsmooth boundary
Piecewise linear planar vector fields
Descripción
Sumario:In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain again at least five limit cycles but now from infinity, which is of monodromic type, and with simpler computations. The proof uses a partial classification of the center problem when both systems are of center type. © 2023, The Author(s).