Mode-Locking in an Infinite Set of Coupled Circle Maps

摘要

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 K/sub c/ is needed for a step to appear. The width of the step behaves as (K-K/sub c/)/sup 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 experimental observations by Sherwin and Zettl that only few true steps exist in I-V characteristics and that in addition to these there are some 'incomplete' steps. (ERA citation 13:058035)