Mode locking in small-world networks of coupled circle maps

We investigate the emergence of mode locking, or frequency synchronization, in a chain of coupled sine-circle maps with randomly distributed parameters, and exhibiting the small-world property. The coupling prescription we adopt considers the nearest and next-to-the-nearest neighbors of a given site, as well as randomly chosen non-local shortcuts, according to a given probability. A transition between synchronized and non-synchronized patterns is observed as this probability is varied. We also study the statistics of the synchronization plateaus, evidencing a Poisson-type distribution.