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Chin. Phys. B, 2015, Vol. 24(5): 054501    DOI: 10.1088/1674-1056/24/5/054501
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Bifurcation for the generalized Birkhoffian system

Mei Feng-Xiang, Wu Hui-Bin
School of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Abstract  

The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.

Keywords:  generalized Birkhoffian system      gradient system      stability      bifurcation  
Received:  14 October 2014      Revised:  20 November 2014      Published:  05 May 2015
PACS:  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  46.40.Ff (Resonance, damping, and dynamic stability)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant No. 11272050).

Corresponding Authors:  Wu Hui-Bin     E-mail:  huibinwu@bit.edu.cn
About author:  45.20.Jj; 46.40.Ff

Cite this article: 

Mei Feng-Xiang, Wu Hui-Bin Bifurcation for the generalized Birkhoffian system 2015 Chin. Phys. B 24 054501

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