  We analyze the dynamics of the order parameter in superconducting open
nanotubes under a strong transport current in an external homogeneous magnetic
field using the time-dependent Ginzburg-Landau equation. Near the critical
transport current, the dissipation processes are driven by vortex and phase
slip dynamics. The transition between the vortex and phase-slip regimes is
found to depend on the external magnetic field only weakly if the magnetic
field and/or the transport current are switched on gradually. In the case of an
abrupt switch-on of the magnetic field or transport current, the system can be
triggered to the stable phase-slip regime, within a certain window of
parameters. Finally, a hysteresis effect in the current-voltage characteristics
is predicted in superconducting open nanotubes.
