  Young solar-type stars rotate rapidly and many are magnetically active; some
undergo magnetic cycles similar to the 22-year solar activity cycle. We conduct
simulations of dynamo action in rapidly rotating suns with the 3D MHD anelastic
spherical harmonic (ASH) code to explore dynamo action achieved in the
convective envelope of a solar-type star rotating at 5 times the current solar
rotation rate. Striking global-scale magnetic wreaths appear in the midst of
the turbulent convection zone and show rich time-dependence. The dynamo
exhibits cyclic activity and undergoes quasi-periodic polarity reversals where
both the global-scale poloidal and toroidal fields change in sense on a roughly
1500 day time scale. These magnetic activity patterns emerge spontaneously from
the turbulent flow and are more organized temporally and spatially than those
realized in our previous simulations of the solar dynamo. We assess in detail
the competing processes of magnetic field creation and destruction within our
simulations that contribute to the global-scale reversals. We find that the
mean toroidal fields are built primarily through an $\Omega$-effect, while the
mean poloidal fields are built by turbulent correlations which are not
necessarily well represented by a simple $\alpha$-effect. During a reversal the
magnetic wreaths propagate towards the polar regions, and this appears to arise
from a poleward propagating dynamo wave. The primary response in the convective
flows involves the axisymmetric differential rotation which shows variations
associated with the poleward propagating magnetic wreaths. In the Sun, similar
patterns are observed in the poleward branch of the torsional oscillations, and
these may represent poleward propagating magnetic fields deep below the solar
surface. [abridged]
