  We present results from simulations of rotating magnetized turbulent
convection in spherical wedge geometry representing parts of the latitudinal
and longitudinal extents of a star. Here we consider a set of runs for which
the density stratification is varied, keeping the Reynolds and Coriolis numbers
at similar values. In the case of weak stratification, we find quasi-steady
dynamo solutions for moderate rotation and oscillatory ones with poleward
migration of activity belts for more rapid rotation. For stronger
stratification, the growth rate tends to become smaller. Furthermore, a
transition from quasi-steady to oscillatory dynamos is found as the Coriolis
number is increased, but now there is an equatorward migrating branch near the
equator. The breakpoint where this happens corresponds to a rotation rate that
is about 3-7 times the solar value. The phase relation of the magnetic field is
such that the toroidal field lags behind the radial field by about $\pi/2$,
which can be explained by an oscillatory $\alpha^2$ dynamo caused by the sign
change of the $\alpha$-effect about the equator. We test the domain size
dependence of our results for a rapidly rotating run with equatorward migration
by varying the longitudinal extent of our wedge. The energy of the axisymmetric
mean magnetic field decreases as the domain size increases and we find that an
$m=1$ mode is excited for a full $2\pi$ azimuthal extent, reminiscent of the
field configurations deduced from observations of rapidly rotating late-type
stars.
