MODE-LOCKING IN COUPLED MAP LATTICES

We study propagation of pulses along one-way coupled map lattices, whi ch originate from the transition between two superstable states of the local map. The velocity of the pulses exhibits a staircase-like behav iour as the coupling parameter is varied. For a piecewise linear local map, we prove that the velocity of the wave has a Devil's staircase d ependence on the coupling parameter. A wave travelling with rational v elocity is found to be stable to parametric perturbations in a manner akin to rational mode-locking for circle maps. We provide evidence tha t mode-locking is also present for a broader range of maps and couplin gs.