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...

Descripción completa

Detalles Bibliográficos
Autores: Itovich, Griselda Rut, Moiola, Jorge Luis
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/105138
Acceso en línea:http://hdl.handle.net/11336/105138
Access Level:acceso abierto
Palabra clave:Period-doubling
Bifurcation
https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
Descripción
Sumario: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.