The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Analisis penduaan Takens-Bogdanov bagi keseimbangan pada asalan dalam persamaan Chua dengan tak linear padu dijalankan. Analisis tempatan menyediakan, dalam anggaran pertama, set bifurkasi yang berbeza, di mana kehadiran beberapa tingkah laku dinamik (termasuk orbit berkala, homoklinik dan heteroklinik) diramalkan. Keputusan tempatan digunakan sebagai panduan untuk menggunakan kaedah berangka yang mencukupi untuk mendapatkan pemahaman global tentang set bifurkasi. Kajian tentang bentuk normal bifurkasi Takens-Bogdanov menunjukkan kehadiran keadaan merosot (kodimensi-tiga), yang dianalisis dalam kedua-dua kes homoklinik dan heteroklinik.
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Salinan
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
Salinan
@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},}
Salinan
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 -