  We show that for rotating harmonically trapped Bose gases in a fractional
quantum Hall state, the anyonic excitation statistics in the rotating gas can
effectively play a {\em dynamical} role. For particular values of the
two-dimensional coupling constant $g = -2\pi \hbar^2 (2k-1)/m$, where $k$ is a
positive integer, the system becomes a noninteracting gas of anyons, with
exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter
equations. Attractive Bose gases under rapid rotation thus can be stabilized in
the thermodynamic limit due to the anyonic statistics of their quasiparticle
excitations.
