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Pàgina inicial > Articles > Articles publicats > Periodic orbits near equilibria via averaging theory of second order |
Data: | 2012 |
Resum: | Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory of first order we established in [1] a similar result for a differential system without assuming the existence of a first integral. Now, using averaging theory of second order, we extend our result to the case when the first order average is identically zero. Our result can be interpreted as a kind of special Hopf bifurcation. |
Ajuts: | Ministerio de Educación y Ciencia MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Nota: | Agraïments: The first and third authors were partially supported by FCT through CAMGSD, Lisbon. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Periodic orbit ; Averaging theory of second order ; Hopf bifurcation |
Publicat a: | Mathematical Modelling and Analysis, Vol. 17 Núm. 5 (2012) , p. 715-731, ISSN 1648-3510 |
Postprint 17 p, 323.7 KB |