On the Analytical Approach of Codimension-Three Degenerate Bogdanov-Takens (B-T) Bifurcation in Satellite Dynamical System
Year: 2023
Author: Muhammad Marwan, Muhammad Zainul Abidin
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 4 : pp. 667–681
Abstract
In this paper, we have conducted parametric analysis on the dynamics of satellite complex system using bifurcation theory. At first, five equilibrium points ε0,1,2,3,4 are symbolically computed in which ε1,3 and ε2,4 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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2023.667
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 4 : pp. 667–681
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Satellite dynamical system Bogdanov-Takens bifurcation normal form generalized eigenvector.