Synchronization on small-world networks
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations and finite-size scaling. Phase synchronization is observed to emerge in the presence of even a tiny fraction P of shortcuts and to display saturated behavior for P ≳ 0.5. This indicates that the same synchronizability as the random network (P=1) can be
... with relatively small number of shortcuts. The transient behavior of the synchronization, obtained from the measurement of the relaxation time, is also discussed.