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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 |
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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. |
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