Bifurcation for the generalized Birkhoffian system

doi:10.1088/1674-1056/24/5/054501

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
Accepted manuscript online:

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 (梅凤翔), Wu Hui-Bin (吴惠彬) Bifurcation for the generalized Birkhoffian system 2015 Chin. Phys. B 24 054501

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