%0 Book Section %1 statphys23_0717 %A Son, S.W. %A Jeong, H. %A Hong, H. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K complex dynamics networks relaxation statphys23 synchronization topic-3 %T Relaxation of synchronization on complex networks %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=717 %X We study collective synchronization in a large number of coupled oscillators on various complex networks. In particular, we pay attention to the relaxation dynamics of synchronization, which is important in the point of view of information transfer or the system recovery dynamics from the perturbation. We measure the relaxation time which takes to establish global synchronization, varying the structural properties of the networks. It is found that the relaxation time in the strong coupling regime ($K>K_c$) exhibits a logarithmic increasing with the network size ($\tau N$), which is attributed to the initial random phase given by $1/N$. Under the removal of initial-phase fluctuation, the relaxation time is found to be independent of the system size, which implies that the local interaction is irrelevant in the relaxation dynamics of the synchronization in the strong coupling regime. The collapsing form of the relaxation dynamics is also derived, and it shows a good consistency with the numerical simulations. As an application, we explore the recovery dynamics of the oscillators when the perturbation comes into the system.

@incollection{statphys23_0717, abstract = {We study collective synchronization in a large number of coupled oscillators on various complex networks. In particular, we pay attention to the relaxation dynamics of synchronization, which is important in the point of view of information transfer or the system recovery dynamics from the perturbation. We measure the relaxation time which takes to establish global synchronization, varying the structural properties of the networks. It is found that the relaxation time in the strong coupling regime ($K>K_c$) exhibits a logarithmic increasing with the network size ($\tau \sim \ln N$), which is attributed to the initial random phase given by $1/\sqrt{N}$. Under the removal of initial-phase fluctuation, the relaxation time is found to be independent of the system size, which implies that the local interaction is irrelevant in the relaxation dynamics of the synchronization in the strong coupling regime. The collapsing form of the relaxation dynamics is also derived, and it shows a good consistency with the numerical simulations. As an application, we explore the recovery dynamics of the oscillators when the perturbation comes into the system.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Son, S.W. and Jeong, H. and Hong, H.}, biburl = {https://www.bibsonomy.org/bibtex/2bf821d8f6e37f9a358435b4acb98b0a3/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {39682426c85fe3e5287a10e49ade3267}, intrahash = {bf821d8f6e37f9a358435b4acb98b0a3}, keywords = {complex dynamics networks relaxation statphys23 synchronization topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:27.000+0200}, title = {Relaxation of synchronization on complex networks}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=717}, year = 2007 }