  Non-equilibrium self-organized patterns formed by particles interacting
through competing range interaction are driven over a substrate by an external
force. We show that, with increasing driving force, the pre-existed static
patterns evolve into dynamic patterns either via disordered phase or depinned
patterns, or via the formation of non-equilibrium stripes. Strikingly, the
stripes are formed either in the direction of the driving force or in the
transverse direction, depending on the pinning strength. The revealed dynamical
patterns are summarized in a dynamical phase diagram.
