  We use the ASH code to model the convective dynamo of solar-type stars. Based
on a series of 15 3-D MHD simulations spanning 4 bins in rotation and mass, we
show what mechanisms are at work in these stellar dynamos with and without
magnetic cycles and how global stellar parameters affect the outcome. We also
derive scaling laws for the differential rotation and magnetic field based on
these simulations. We find a weaker trend between differential rotation and
stellar rotation rate, ($\Delta \Omega \sim (|\Omega|/\Omega_{\odot})^{0.46}$)
in the MHD solutions than in their HD counterpart
$(|\Omega|/\Omega_{\odot})^{0.66})$, yielding a better agreement with the
observational trends based on power laws. We find that for a fluid Rossby
number between $0.15 \lesssim Ro_f \lesssim 0.65$ the solutions possess long
magnetic cycle, if $Ro_f \lesssim 0.42$ a short cycle and if $Ro_f \gtrsim 1$
(anti-solar-like differential rotation) a statistically steady state. We show
that short-cycle dynamos follow the classical Parker-Yoshimura rule whereas the
long-cycle period ones do not. We further demonstrate that the Rossby number
dependency of the large-scale surface magnetic field in the simulation
($B_{L,surf} \sim Ro_{f}^{-1.26}$) agrees better with observations ($B_{V} \sim
Ro_{s}^{-1.4 \pm 0.1}$) and differs from dynamo scaling based on the global
magnetic energy ($B_{bulk} \sim Ro_{f}^{-0.5}$). We also show that up to few
percents of the stellar luminosity can be channelled into the star's magnetism,
hence providing a large energy reservoir for possible surface eruptive events.
