  We study the differential resistivity transition of two-dimensional
superconducting arrays induced by an external driving current, in the presence
of thermal fluctuations and a magnetic field corresponding to $f$ flux quantum
per plaquette. Recent experiments have identified this transition as a dynamic
vortex Mott insulator transition at vortex densities near rational values of
$f$. The critical behavior is determined from a scaling analysis of the
current-voltage relation near the transition, obtained by Monte Carlo
simulations of a Josephson-junction array model in the vortex representation.
For a square-lattice array, the critical exponents obtained near $f=1/2$ are
consistent with the experimental observations. The same scaling behavior is
observed near $f=1/3$. For a honeycomb array, although similar results are
obtained for $f=1/3$, the transition is absent for $f=1/2$, consistent with an
incommensurate vortex phase.
