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We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters that 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 > or similar to 0.5. This indicates that the same synchronizability as the random network (P=1) can be achieved with relatively small number of shortcuts. The transient behavior of the synchronization, obtained from the measurement of the relaxation time, is also discussed.
Hong et al. (Thu,) studied this question.