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

 

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Opened Access On the Takens-Bogdanov Bifurcation in the Chua’s Equation
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Author: Algaba Durán, Antonio
Freire Macías, Emilio
Gamero Gutiérrez, Estanislao
Rodriguez Luis, Alejandro José
Department: Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Date: 1999
Published in: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E82-A (9), 1722-1728.
Document type: Article
Abstract: 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.
Cite: Algaba Durán, A., Freire Macías, E., Gamero Gutiérrez, E. y Rodriguez Luis, A.J. (1999). On the Takens-Bogdanov Bifurcation in the Chua’s Equation. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E82-A (9), 1722-1728.
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URI: http://hdl.handle.net/11441/58672

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