Synchronization on small-world networks.
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
H
H
Department of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea.
Choi
M Y
MY
Kim
Beom Jun
BJ