  We present results from compressible Cartesian convection simulations with
and without imposed shear. In the former case the dynamo is expected to be of
$\alpha^2\varOmega$ type which is generally expected to be relevant for the
Sun, whereas the latter case refers to $\alpha^2$ dynamos which are more likely
to occur in more rapidly rotating stars whose differential rotation is small.
We perform a parameter study where the shear flow and the rotational influence
are varied to probe the relative importance of both types of dynamos.
Oscillatory solutions are preferred both in the kinematic and saturated regimes
when the negative ratio of shear to rotation rates, $q\equiv -S/\varOmega$, is
between 1.5 and 2, i.e., when shear and rotation are of comparable strengths.
Other regions of oscillatory solutions are found with small values of $q$,
i.e., when shear is weak in comparison to rotation, and in the regime of large
negative $q$s, when shear is very strong in comparison to rotation. However,
exceptions to these rules also appear so that for a given ratio of shear to
rotation, solutions are non-oscillatory for small and large shear, but
oscillatory in the intermediate range. Changing the boundary conditions from
vertical field to perfect conductor ones changes the dynamo mode from
oscillatory to quasi-steady. Furthermore, in many cases an oscillatory solution
exists only in the kinematic regime whereas in the nonlinear stage the mean
fields are stationary. However, the cases with rotation and no shear are always
oscillatory in the parameter range studied here and the dynamo mode does not
depend on the magnetic boundary conditions. The strengths of total and
large-scale components of the magnetic field in the saturated state, however,
are sensitive to the chosen boundary conditions.
