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Piecewise linear differential systems with two real saddles
Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Medrado, Joao Carlos (Universidade Federal de Goiás(Brazil).Instituto de Matemática e Estatística)
Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)

Data: 2013
Resum: 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.
Nota: Número d'acord de subvenció MCYT/MTM2008-03437
Nota: Número d'acord de subvenció AGAUR/2009/SGR-410
Nota: Agraïments: All authors are also supported by the joint project CAPES–MECD grant PHB-2009-0025–PCand AUXPE–DGU 15/2010.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Non–smooth differential system ; Limit cycle ; Piecewise linear differential system ; Hopf bifurcation ; Sliding limit cycle
Publicat a: Mathematics and Computers in Simulation, Vol. 95 (2013) , p. 13-22, ISSN 0378-4754

DOI: 10.1016/j.matcom.2013.02.007

12 p, 272.4 KB

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