Limit cycles of discontinuous piecewise polynomial vector fields

Web of Science: 4 cites, Scopus: 4 cites, Google Scholar: cites

(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tonon, Durval José.

(University of Goiás (Brasil). Institute of Mathematics and Statistics of Federal)

Data:	2017
Resum:	When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x= -y((x^2 y^2)/2)^m and y= x((x^2 y^2)/2)^m with m 1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.
Ajuts:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P
Nota:	Agraïments: The first author is partially supported by a FAPESP/Brazil grant number 2014/02134-7, a CNPq-Brazil grant number 443302/2014-6 and CAPES grants 88881.030454/2013-01 (from the program CSF-PVE) and 1576689 (from the program PNPD). The second author is partially supported by the CAPES grant 88881.030454/2013-01 from the program CSF-PVE. D.J. Tonon is supported by grant #2012/10 26 7000 803, Goiás Research Foundation (FAPEG), PROCAD/CAPES grant 88881.068462/2014-01 and by CNPq-Brazil.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Averaging theory ; Limit cycles ; Piecewise smooth vector fields
Publicat a:	Journal of mathematical analysis and applications, Vol. 449 Núm. 1 (2017) , p. 572-579, ISSN 1096-0813

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Registre creat el 2017-11-28, darrera modificació el 2022-02-06