Limit cycles for discontinuous quadratic differential systems with two zones
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mereu, Ana Cristina (UFSCar(Brazil). Department of Physics, Chemistry and Mathematics)

Date:	2014
Abstract:	In this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems, which can bifurcate from the periodic orbits of the quadratic isochronous centers ˙x = −y + x2, ˙y = x + xy and ˙x = −y + x2 − y2, y˙ = x + 2xy when they are perturbed inside the class of all discontinuous quadratic polynomial differential systems with the straight line of discontinuity y = 0. Comparing the obtained results for the discontinuous with the results for the continuous quadratic polynomial differential systems, this work shows that the discontinuous systems have at least 3 more limit cycles surrounding the origin than the continuous ones.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338
Note:	Agraïments: The second author is partially supported by a FAPESP-BRAZIL grant 2012/20884-8. Both authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Discontinuous quadratic systems ; Averaging theory ; Isochronous center
Published in:	Journal of mathematical analysis and applications, Vol. 413 Núm. 2 (2014) , p. 763-775, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2013.12.031

Postprint 14 p, 650.4 KB

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