We present simulations of the dynamics of underdamped classical Joseph
son arrays for values of the flux quanta per unit cell f=1/2. We find
the dynamics of this system to be quite rich. The I-V characteristics
are found to have two distinct regime as the damping is increased. At
low voltages the current-voltage characteristics exhibit a regime whic
h we characterize as flux-flow-like since it is dominated by the motio
n of the vortex superlattice. This regime may exhibit chaotic-like beh
avior as the damping parameter is increased. At high voltages the char
acteristics jump to an ohmic-like state in which the junctions are all
oscillating. We present a potential model which is quite useful in un
derstanding the dynamics of the system.