On the Takens-Bogdanov Bifurcation in the Chua’s Equation

The analysis of the Takens-Bogdanov bifurcation of the equilibrium at the origin in the Chua’s equation with a cubic nonlinearity is carried out. The local analysis provides, in first approximation, different bifurcation sets, where the presence of several dynamical behaviours (including periodic, h...

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Detalles Bibliográficos
Autores: Algaba Durán, Antonio, Freire Macías, Emilio, Gamero Gutiérrez, Estanislao, Rodríguez Luis, Alejandro José
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1999
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/58672
Acceso en línea:http://hdl.handle.net/11441/58672
Access Level:acceso abierto
Palabra clave:Bifurcations
Oscillations
Chua circuit
Descripción
Sumario:The analysis of the Takens-Bogdanov bifurcation of the equilibrium at the origin in the Chua’s equation with a cubic nonlinearity is carried out. The local analysis provides, in first approximation, different bifurcation sets, where the presence of several dynamical behaviours (including periodic, homoclinic and heteroclinic orbits) is predicted. The local results are used as a guide to apply the adequate numerical methods to obtain a global understanding of the bifurcation sets. The study of the normal form of the Takens-Bogdanov bifurcation shows the presence of a degenerate (codimension-three) situation, which is analyzed in both homoclinic and heteroclinic cases.