J. Nonl. Mod. Anal., 5 (2023), pp. 667-681.
Published online: 2023-12
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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} }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.