  A two-dimensional rapidly rotating Bose-Einstein condensate in a harmonic
plus quartic trap is expected to have unusual vortex states that do not occur
in a pure harmonic trap. At a critical rotation speed $\Omega_h$, a central
hole appears in the condensate, and at some faster rotation speed $\Omega_g$,
the system undergoes a transition to a giant vortex state with pure
irrotational flow. Using a time-dependent variational analysis, we study the
behavior of an annular condensate with a single concentric ring of vortices.
The transition to a giant vortex state is investigated by comparing the energy
of the two equilibrium states (the ring of vortices and the giant vortex) and
also by studying the dynamical stability of small excitation modes of the ring
of vortices.
