On period doubling bifurcations of cycles and the harmonic balance method
This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2006 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/105138 |
| Acesso em linha: | http://hdl.handle.net/11336/105138 |
| Access Level: | acceso abierto |
| Palavra-chave: | Period-doubling Bifurcation https://purl.org/becyt/ford/2.2 https://purl.org/becyt/ford/2 |
| Resumo: | This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method. |
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