  In this paper, we shall study the dynamical behavior of the universe
accelerated by the so called Veneziano ghost dark energy component locally and
globally by using the linearization and nullcline method developed in this
paper. The energy density is generalized to be proportional to the Hawking
temperature defined on the trapping horizon instead of Hubble horizon of the
Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the
fate of the universe and present the bifurcation phenomenon of the dynamical
system of the universe. It seems that the universe could be dominated by dark
energy at present in some region of the parameter space.
