title: Synchronization on small-world networks.
abstract: 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.
authors.affiliation: Department of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea.
authors.forename: H
authors.initials: H
authors.lastname: Hong
authors.forename: M Y
authors.initials: MY
authors.lastname: Choi
authors.forename: Beom Jun
authors.initials: BJ
authors.lastname: Kim