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

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.