Manifold stability of equilibrium state of autonomous generalized Birkhoff system

Manifold stability of equilibrium state of autonomous generalized Birkhoff system is studied. The perturbation equation and equilibrium equation of autonomous generalized Birkhoff system is established. The corresponding criteria for manifold stability of autonomous generalized Birkhoff system is given by the Liapunov stability theory. Finally, an example is presented to illustrate these results.