News & Announcements
Links
On the Analytical Approach of Codimension-Three Degenerate Bogdanov-Takens (B-T) Bifurcation in Satellite Dynamical System
  
View Full Text  View/Add Comment  Download reader
KeyWord:Satellite dynamical system, Bogdanov-Takens bifurcation, normal form, generalized eigenvector
Author NameAffiliation
Muhammad Marwan College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Muhammad Zainul Abidin College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Hits: 119
Download times: 156
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.