  We carry out systematic and high-resolution studies of dynamo action in a
shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the
magnetic Prandtl number $Pr_{\rm M}$ and the magnetic Reynolds number $Re_{\rm
M}$. Our study suggests that it is natural to think of dynamo onset as a
nonequilibrium, first-order phase transition between two different turbulent,
but statistically steady, states. The ratio of the magnetic and kinetic
energies is a convenient order parameter for this transition. By using this
order parameter, we obtain the stability diagram (or nonequilibrium phase
diagram) for dynamo formation in our MHD shell model in the $(Pr^{-1}_{\rm M},
Re_{\rm M})$ plane. The dynamo boundary, which separates dynamo and no-dynamo
regions, appears to have a fractal character. We obtain hysteretic behavior of
the order parameter across this boundary and suggestions of nucleation-type
phenomena.
