A second order analysis of the periodic solutions for nonlinear periodic differential systems with a small parameter
We deal with nonlinear T-periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions. We provide the expressions of the bifurcation functions up to second order in the small parameter in order that their simple zeros are initia...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150518 |
| Acceso en línea: | https://ddd.uab.cat/record/150518 https://dx.doi.org/urn:doi:10.1016/j.physd.2011.11.007 |
| Access Level: | acceso abierto |
| Palabra clave: | Periodic solution Averaging method Lyapunov-Schmidt reduction |
| Sumario: | We deal with nonlinear T-periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions. We provide the expressions of the bifurcation functions up to second order in the small parameter in order that their simple zeros are initial values of the periodic solutions that persist after the perturbation. In the end two applications are done. The key tool for proving the main result is the Lyapunov-Schmidt reduction method applied to the T-Poincaré-Andronov mapping. |
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