  In a simple model we investigate three competing orders: d-wave
superconductivity, spin and orbital antiferromagnetism (AF) in the vicinity of
a single vortex in a cuprate superconductor. We find that when the potential
for the orbital AF $V_{d}$ is comparatively small, the spin-density-wave (SDW)
order has an enhancement at the vortex core center, and the ''d-density-wave''
(DDW) order exhibits a rather weak behavior around the core and vanishing small
away from the core. However, when $V_{d}$ becomes large, globally, the SDW
order decreases and the DDW order increases; locally, not only the peak of the
SDW order around the core still exists, though relatively suppressed, but also
a local peak for the DDW order finally appears. Similar effects are also
revealed for the features when varying doping. Comparisons with experiments are
discussed.
