New results on averaging theory and applications
The usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i.e. the Jacobian of the averaged function in it is zero, the classical av...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:169475 |
| Acesso em linha: | https://ddd.uab.cat/record/169475 https://dx.doi.org/urn:doi:10.1007/s00033-016-0682-7 |
| Access Level: | acceso abierto |
| Palavra-chave: | Averaging theory Fitzhugh--Nagumo system Lorenz system Polynomial differential system |
| Resumo: | The usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i.e. the Jacobian of the averaged function in it is zero, the classical averaging theory does not provide information about the periodic solution associated to a non simple zero. Here we provide sufficient conditions in order that the averaging theory can be applied also to non simple zeros for studying their associated periodic solutions. Additionally we do two applications of this new result for studying the zero--Hopf bifurcation in the Lorenz system and in the Fitzhugh--Nagumo system. |
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