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

Muhammad Marwan; Muhammad Zainul Abidin

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

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KeyWord:Satellite dynamical system, Bogdanov-Takens bifurcation, normal form, generalized eigenvector

Author Name	Affiliation
Muhammad Marwan	College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, Zhejiang 321004, China
Muhammad Zainul Abidin	College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, Zhejiang 321004, China

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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

$\mathcal{E}_{0,1,2,3,4}$ are symbolically computed in which

$\mathcal{E}_{1,3}$ and

$\mathcal{E}_{2,4}$ 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

$\alpha_{2}=0$ is observed, which confirms all the discussed cases belong to a codimension-three bifurcation along with degeneracy conditions.