Volume 5, Issue 4
On the Analytical Approach of Codimension-Three Degenerate Bogdanov-Takens (B-T) Bifurcation in Satellite Dynamical System

Muhammad Marwan & Muhammad Zainul Abidin

J. Nonl. Mod. Anal., 5 (2023), pp. 667-681.

Published online: 2023-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we have conducted parametric analysis on the dynamics of satellite complex system using bifurcation theory. At first, five equilibrium points $\varepsilon_{0,1,2,3,4}$ are symbolically computed in which $\varepsilon_{1,3}$ and $\varepsilon_{2,4}$ are symmetric. Then, several theorems are stated and proved for the existence of B-T bifurcation on all equilibrium points with the aid of generalized eigenvectors and practical formulae instead of linearizations. Moreover, a special case $α_2 = 0$ is observed, which confirms all the discussed cases belong to a codimension-three bifurcation along with degeneracy conditions.

  • AMS Subject Headings

37G99, 34C23, 37L10

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COPYRIGHT: © Global Science Press

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@Article{JNMA-5-667, author = {Marwan , Muhammad and Abidin , Muhammad Zainul}, title = {On the Analytical Approach of Codimension-Three Degenerate Bogdanov-Takens (B-T) Bifurcation in Satellite Dynamical System}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {4}, pages = {667--681}, abstract = {

In this paper, we have conducted parametric analysis on the dynamics of satellite complex system using bifurcation theory. At first, five equilibrium points $\varepsilon_{0,1,2,3,4}$ are symbolically computed in which $\varepsilon_{1,3}$ and $\varepsilon_{2,4}$ are symmetric. Then, several theorems are stated and proved for the existence of B-T bifurcation on all equilibrium points with the aid of generalized eigenvectors and practical formulae instead of linearizations. Moreover, a special case $α_2 = 0$ is observed, which confirms all the discussed cases belong to a codimension-three bifurcation along with degeneracy conditions.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.667}, url = {http://global-sci.org/intro/article_detail/jnma/22200.html} }
TY - JOUR T1 - On the Analytical Approach of Codimension-Three Degenerate Bogdanov-Takens (B-T) Bifurcation in Satellite Dynamical System AU - Marwan , Muhammad AU - Abidin , Muhammad Zainul JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 667 EP - 681 PY - 2023 DA - 2023/12 SN - 5 DO - http://doi.org/10.12150/jnma.2023.667 UR - https://global-sci.org/intro/article_detail/jnma/22200.html KW - Satellite dynamical system, Bogdanov-Takens bifurcation, normal form, generalized eigenvector. AB -

In this paper, we have conducted parametric analysis on the dynamics of satellite complex system using bifurcation theory. At first, five equilibrium points $\varepsilon_{0,1,2,3,4}$ are symbolically computed in which $\varepsilon_{1,3}$ and $\varepsilon_{2,4}$ are symmetric. Then, several theorems are stated and proved for the existence of B-T bifurcation on all equilibrium points with the aid of generalized eigenvectors and practical formulae instead of linearizations. Moreover, a special case $α_2 = 0$ is observed, which confirms all the discussed cases belong to a codimension-three bifurcation along with degeneracy conditions.

Muhammad Marwan & Muhammad Zainul Abidin. (2023). On the Analytical Approach of Codimension-Three Degenerate Bogdanov-Takens (B-T) Bifurcation in Satellite Dynamical System. Journal of Nonlinear Modeling and Analysis. 5 (4). 667-681. doi:10.12150/jnma.2023.667
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