Mode locking in an infinite set of coupled circle maps

We show that the mode locking in coupled circle maps with random phases is very different from that in a single circle map. A finite nonlinearity Kc is needed for a step to appear. The width of the step behaves as (K-Kc{)}²$. The complete mode locking (at K=1 for uncoupled maps) behaves singularly as the coupling is turned on. We argue that our model describes the mode locking in charge-density-wave materials. Our results are in qualitative agreement with the experimental observation by Sherwin and Zettl that only few true steps exist in the I-V characteristics and that in addition to these there are some ``incomplete'' steps.