Synchronization on small-world networks

Details Synchronization on small-world networks Synchronization on small-world networks

2001-10-18

arxiv.org/abs/cond-mat/0110359v1

Phys. Rev. E 65, 026139 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevE.65.026139

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 $P \gtrsim 0.5$. 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.

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