  Coronal magnetic flux ropes are closely related to large-scale solar
activities. Using a 2.5-dimensional time-dependent ideal magnetohydrodynamic
(MHD) model in Cartesian coordinates, we carry out numerical simulations to
investigate the evolution of a magnetic system consisting of a flux rope
embedded in a fully-closed quadrupolar magnetic field with different
photospheric flux distributions. It is found that, when the photospheric flux
is not concentrated too much towards the polarity inversion line (PIL) and the
constraint exerted by the background field is not too weak, the equilibrium
states of the system are divided into two branches: the rope sticks to the
photosphere for the lower branch and levitates in the corona for the upper
branch. These two branches are connected by an upward catastrophe (from the
lower branch to the upper) and a downward catastrophe (from the upper branch to
the lower). Our simulations reveal that there exist both upward and downward
catastrophes in quadrupolar fields, which may be either force-free or
non-force-free. The existence and the properties of these two catastrophes are
influenced by the photospheric flux distribution, and a downward catastrophe is
always paired with an upward catastrophe. Comparing the decay indices in
catastrophic and non-catastrophic cases, we infer that torus unstable might be
a necessary but not sufficient condition for a catastrophic system.
