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| Home > Articles > Published articles > Birth of limit cycles for a classe of continuous and discontinuous differential systems in (d 2)-dimension |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)| Date: | 2016 |
| Abstract: | The orbits of the reversible differential system ˙x = −y, ˙y = x, ˙z = 0, with x, y ∈ R and z ∈ R d, are periodic with the exception of the equilibrium points (0, 0, z1, . . . , zd). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ˙x = −y, ˙y = x, ˙z = 0, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y > 0 and the other in y < 0. In the first case this maximum number is nd(n − 1)/2, and in the second is nd(n − 1). |
| 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: FEDER/UNAB10-4E-378. The second author is partially supported by a FAPESP-BRAZIL grant 2012/18780-0. The third author is partially supported by a FAPESP-BRAZIL grant 2012/23591-1 and 2013/21078-8. |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Subject: | Averaging theory ; Discontinuous polynomial differential system ; Limit cycle ; Periodic orbit |
| Published in: | Dynamical Systems, Vol. 31 Núm. 3 (2016) , p. 237-250, ISSN 1468-9375 |
16 p, 737.1 KB |
