中国物理B ›› 2015, Vol. 24 ›› Issue (5): 54501-054501.doi: 10.1088/1674-1056/24/5/054501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Bifurcation for the generalized Birkhoffian system

梅凤翔, 吴惠彬   

  1. School of Mathematics, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2014-10-14 修回日期:2014-11-20 出版日期:2015-05-05 发布日期:2015-05-05
  • 基金资助:

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

Bifurcation for the generalized Birkhoffian system

Mei Feng-Xiang (梅凤翔), Wu Hui-Bin (吴惠彬)   

  1. School of Mathematics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2014-10-14 Revised:2014-11-20 Online:2015-05-05 Published:2015-05-05
  • Contact: Wu Hui-Bin E-mail:huibinwu@bit.edu.cn
  • About author:45.20.Jj; 46.40.Ff
  • Supported by:

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

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摘要：

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.

关键词: generalized Birkhoffian system, gradient system, stability, bifurcation

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.

Key words: generalized Birkhoffian system, gradient system, stability, bifurcation

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
46.40.Ff (Resonance, damping, and dynamic stability)