Averaging approach to cyclicity of Hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems

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(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Zhang, Weinian (Sichuan University (Xina). Department of Mathematics)

Fecha:	2017
Resumen:	It is well known that the cyclicity of a Hopf bifurcation in continuous quadratic polynomial differential systems in \R^2 is 3. In contrast here we consider discontinuous differential systems in \R^2 defined in two half--planes separated by a straight line. In one half plane we have a general linear center at the origin of \R^2, and in the other a general quadratic polynomial differential system having a focus or a center at the origin of \R^2. Using averaging theory, we prove that the cyclicity of a Hopf bifurcation for such discontinuous differential systems is at least 5. Our computations show that only one of the averaged functions of fifth order can produce 5 limit cycles and there are no more limit cycles up to sixth order averaged function.
Ayudas:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2016-77278-P
Nota:	Agraïments: The first author is supported by NSFC grant #11471228. The third author is supported by NSFC grants #11231001, #11221101.
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió acceptada per publicar
Materia:	Cyclicity ; Discontinuous differential system ; Hopf bifurcation ; Limit cycles
Publicado en:	Discrete and continuous dynamical systems. Series B, Vol. 22 Núm. 10 (2017) , p. 3953-3965, ISSN 1553-524X

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Registro creado el 2017-11-28, última modificación el 2022-05-27