  Motivated by a recent experiment [K.C. Wright et. al. Phys. Rev. Lett. 110,
025302 (2013)], we investigate deterministic discontinuous jumps between
quantized circulation states in a toroidally trapped Bose-Einstein condensate.
These phase slips are induced by vortex excitations created by a rotating weak
link. We analyze influence of a localized condensate density depletion and
atomic superflows, governed by the rotating barrier, on the energetic and
dynamical stability of the vortices in the ring-shaped condensate. We simulate
in a three-dimensional dissipative mean field model the dynamics of the
condensate using parameters similar to the experimental conditions. Moreover,
we consider the dynamics of the stirred condensate far beyond the
experimentally explored region and reveal surprising manifestations of complex
vortex dynamics.
