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

Antonio ALGABA  Emilio FREIRE  Estanislao GAMERO  Alejandro J. RODRIGUEZ-LUIS  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.9   pp.1722-1728
Publication Date: 1999/09/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
bifurcation,  oscillations,  Chua's circuit,  

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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.