  We experimentally and theoretically study the response of a superradiant or
bad-cavity laser to an applied coherent drive. We observe two forms of
synchronization (injection locking) between the superradiant ensemble and the
applied drive: one attractive and one repulsive in nature. We explain the
region of repulsion as arising from the higher three-dimensional description of
the atomic spin state that stores the laser coherence in a superradiant laser,
as opposed to a two-parameter description of the electric field in a
traditional good-cavity laser. We derive a phase diagram of predicted behavior
and experimentally measure the response of the system across various
trajectories therein.
