Using advection to control the velocity of patterns in rings of maps

Traveling patterns are well-known features of rings of symmetrically coupled maps which, however, propagate with rather small velocities, of the order of ∼10−3 sites per step. We show that it is easy to produce traveling patterns with velocities tunable over three orders of magnitude by simply breaking the symmetry of the coupling between neighbors. This asymmetry arises naturally when the usual model of coupled map lattices is generalized to also include advection. In addition, asymmetries change the wavelength of waves traveling on the lattice.