  Large-scale solar eruptive activities have a close relationship with coronal
magnetic flux ropes. Previous numerical studies have found that the equilibrium
of a coronal flux rope system could be disrupted if the axial magnetic flux of
the rope exceeds a critical value, so that the catastrophe occurs, initiating
the flux rope to erupt. Further studies discovered that the catastrophe does
not necessarily exist: the flux rope system with certain photospheric flux
distributions could be non-catastrophic. It is noteworthy that most previous
numerical studies are under the ideal magnetohydrodynamic (MHD) condition, so
that it is still elusive whether there is the catastrophe associated with the
critical axial flux if magnetic reconnection is included in the flux rope
system. In this paper, we carried out numerical simulations to investigate the
evolutions of coronal magnetic rope systems under the ideal MHD and the
resistive condition. Under the ideal MHD condition, our simulation results
demonstrate that the flux rope systems with either too compact or too weak
photospheric magnetic source regions are non-catastrophic versus varying axial
flux of the rope, and thus no eruption could be initiated; if there is magnetic
reconnection in the rope system, however, those flux rope systems could change
to be capable of erupting via the catastrophe associated with increasing axial
flux. Therefore, magnetic reconnection could significantly influence the
catastrophic behaviors of flux rope system. It should be both the magnetic
topology and the local physical parameters related to magnetic reconnection
that determine whether the increasing axial flux is able to cause flux rope
eruptions.
