  Late-type stars rotate differentially owing to anisotropic turbulence in
their outer convection zones. The rotation is called solar-like (SL) when the
equator rotates fastest and anti-solar (AS) otherwise. Hydrodynamic simulations
show a transition from SL to AS rotation as the influence of rotation on
convection is reduced, but the opposite transition occurs at a different point
in the parameter space. The system is bistable, i.e., SL and AS rotation
profiles can both be stable. We study the effect of a dynamo-generated magnetic
field on the large-scale flows, particularly on the possibility of bistable
behavior of differential rotation. We solve the hydromagnetic equations
numerically in a rotating spherical shell for a set of different radiative
conductivities controlling the relative importance of convection. In agreement
with earlier findings, our models display SL rotation profiles when the
rotational influence on convection is strong and a transition to AS when the
rotational influence decreases. We find that dynamo-generated magnetic fields
help to produce SL differential rotation compared to the hydrodynamic
simulations. We do not observe any bistable states of differential rotation. In
the AS cases we get coherent single-cell meridional circulation, whereas in SL
cases we get multi-cellular patterns. In both cases, we obtain poleward
circulation near the surface with a magnitude close to that observed in the
Sun. Moreover, both differential rotation and meridional circulation have
significant magnetic cycle-related variations that are similar in strength to
those of the Sun. Purely hydrodynamic simulations of differential rotation and
meridional circulation are shown to be of limited relevance as magnetic fields,
self-consistently generated by dynamo action, significantly affect the flows.
