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.
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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