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| Pàgina inicial > Articles > Articles publicats > Limit cycles bifurcanting from the period annulus of a uniform isochronous center in a quartic polynomial differential system |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Data: | 2015 |
| Resum: | We study the number of limit cycles that bifurcate from the periodic solutions surrounding a uniform isochronous center located at the origin of the quartic polynomial differential system =-y xy(x^2 y^2), =x y^2(x^2 y^2), when it is perturbed inside the class of all quartic polynomial differential systems. Using the averaging theory of first order we show that at least 8 limit cycles can bifurcate from the period annulus of the considered center. Recently this problem was studied in Electron. J. Differ. Equ. 95 (2014), 1--14 where the authors only found 3 limit cycles. |
| Ajuts: | Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338 |
| Nota: | Agraïments: The first author is supported by a Ciência sem Fronteiras-CNPq grant number 201002/ 2012-4 MINECO/FEDER grant UNAB13-4E-1604, and a CAPES grant number 88881.030454/2013-01 from the program CSF-PVE. |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Matèria: | Averaging theory ; Limit cycles ; Periodic orbit ; Polynomial vector field ; Uniform isochronous center |
| Publicat a: | Electronic journal of differential equations, Vol. 2015 Núm. 246 (2015) , p. 11, ISSN 1072-6691 |
13 p, 609.8 KB |
