  We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette
flow - flow confined between two concentric independently rotating cylinders -
consider small aspect ratio by solving the ferrohydrodynamical equations,
carrying out systematic bifurcation analysis. Without magnetic field, we find
steady flow patterns, previously observed with a simple fluid, such as those
containing normal one- or two vortex cells, as well as anomalous one-cell and
twin-cell flow states. However, when a symmetry-breaking transverse magnetic
field is present, all flow states exhibit stimulated, finite two-fold mode.
Various bifurcations between steady and unsteady states can occur,
corresponding to the transitions between the two-cell and one-cell states.
While unsteady, axially oscillating flow states can arise, we also detect the
emergence of new unsteady flow states. In particular, we uncover two new
states: one contains only the azimuthally oscillating solution in the
configuration of the twin-cell flow state, and another a rotating flow state.
Topologically, these flow states are a limit cycle and a quasiperiodic solution
on a two-torus, respectively. Emergence of new flow states in addition to
observed ones with classical fluid, indicates that richer but potentially more
controllable dynamics in ferrofluidic flows, as such flow states depend on the
external magnetic field.
