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 - <p style="text-align: justify;">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.</p>