Limit cycles for a class of continuous and discontinuous cubic polynomial differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Lopes, Bruno D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
De Moraes, Jaime Rezende (IBILCE-UNESP(Brazil). Departamento de Matemática)

Date:	2014
Abstract:	We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers x˙ = y(−1 + 2αx + 2βx2), y˙ = x + α(y2 − x2) + 2βxy2, α ∈ R, β < 0, when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems. We obtain that the maximum number of limit cycles which can be obtained by the averaging method of first order is 3 for the perturbed continuous systems and for the perturbed discontinuous systems at least 12 limit cycles can appear.
Grants:	Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338 European Commission 318999
Note:	Agraïments: FEDER-UNAB10-4E-378. The first and second author are supported by CAPES-MECD grant PHB-2009-0025-PC. The third author is supported by FAPESP-2010/17956-1.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Isochronous center ; Limit cycles ; Periodic orbit ; Polynomial vector field
Published in:	Qualitative theory of dynamical systems, Vol. 13 Núm. 1 (2014) , p. 129-148, ISSN 1662-3592

DOI: 10.1007/s12346-014-0109-9

Postprint 19 p, 640.1 KB

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