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

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

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

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

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.9 pp.1722-1728

Publication Date: 1999/09/25

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Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)

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Antonio ALGABA, Emilio FREIRE, Estanislao GAMERO, Alejandro J. RODRIGUEZ-LUIS, "On the Takens-Bogdanov Bifurcation in the Chua's Equation" in IEICE TRANSACTIONS on Fundamentals, vol. E82-A, no. 9, pp. 1722-1728, September 1999, doi: .
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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_9_1722/_p

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@ARTICLE{e82-a_9_1722,
author={Antonio ALGABA, Emilio FREIRE, Estanislao GAMERO, Alejandro J. RODRIGUEZ-LUIS, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Takens-Bogdanov Bifurcation in the Chua's Equation},
year={1999},
volume={E82-A},
number={9},
pages={1722-1728},
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.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - On the Takens-Bogdanov Bifurcation in the Chua's Equation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1722
EP - 1728
AU - Antonio ALGABA
AU - Emilio FREIRE
AU - Estanislao GAMERO
AU - Alejandro J. RODRIGUEZ-LUIS
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1999
AB - 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.
ER -