  We numerically study the symmetry breaking instabilities of vortex patterns
in a rotating harmonic potential using a type of Ginzburg-Landau equation. The
configurations of vortex lattices change markedly by the symmetry-breaking
instabilities, and then, some vortices move away from the confinement
potential, which leads to the annihilation of vortices. The symmetry-breaking
instabilities and the instabilities of vortex nucleation determine the
parameter region of stable vortex patterns. We verify that the
symmetry-breaking instabilities also occur in a type of complex Ginzburg-Landau
equation.
