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Pàgina inicial > Articles > Articles publicats > Limit cycles bifurcating from the periodic orbits of a discontinuous piecewise linear differential center with two zones |
Data: | 2015 |
Resum: | We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0 we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that its is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential systems formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N ≥ 2 when p is a real or virtual center. |
Ajuts: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 |
Nota: | Agraïments: FEDER-UNAB 10-4E-378. The second author is partially supported by a FAPESP-BRAZIL grant 2013/16492-0. The third authors is partially supported by a FAPESP-BRAZIL grant 2012/18780-0. The three authors are also supported by a CAPES CSF-PVE grant 88881.030454/ 2013-01 from the program CSF-PVE. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Discontinuous differential system ; Limit cycles ; Piecewise linear differential system |
Publicat a: | International journal of bifurcation and chaos in applied sciences and engineering, Vol. 25 Núm. 11 (2015) , p. 1550144 (11 pages), ISSN 1793-6551 |
Postprint 15 p, 389.8 KB |