  We investigate the driven states of a two-dimensional crystal whose ground
state can be tuned through a square-triangular transition. The depinning of
such a system from a quenched random background potential occurs via a complex
sequence of dynamical states, which include plastic flow states, hexatics,
dynamically stabilized triangle and square phases and intermediate regimes of
phase coexistence. These results are relevant to transport experiments in the
mixed phase of several superconductors which exhibit such structural
transitions as well as to driven colloidal systems whose interactions can be
tuned via surface modifications.
