Piecewise linear differential systems with two real saddles

In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to a...

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Detalles Bibliográficos
Autores: Artés Ferragud, Joan Carles|||0000-0003-4332-7495, Llibre, Jaume|||0000-0002-9511-5999, Medrado, Joao Carlos|||0000-0001-5042-9110, 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:150653
Acceso en línea:https://ddd.uab.cat/record/150653
https://dx.doi.org/urn:doi:10.1016/j.matcom.2013.02.007
Access Level:acceso abierto
Palabra clave:Non-smooth differential system
Limit cycle
Piecewise linear differential system
Hopf bifurcation
Sliding limit cycle
Descripción
Sumario:In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to another segment of the same line, and this produces a generalized singular point on the line. This point is a focus or a center and there can be found limit cycles around it. We are going to show that the maximum number of limit cycles that can bifurcate from this focus is two. One of them appears through a Hopf bifurcation and the second when the focus becomes a node by means of the sliding.