Statistics of Extreme Fluctuations in SmallWorld Synchronized Systems
Abstract
We study the statistics and the scaling of the extreme fluctuations in smallworldcoupled interacting systems with relaxational dynamics(H. Guclu and G. Korniss, condmat/0311575 (2003).). After introducing random links to a onedimensional lattice, the average size of the fluctuations becomes finite (synchronized state) and the typical size of the extreme fluctuations diverges only logarithmically in the large systemsize limit. This weak logarithmic divergence ensures synchronization in a practical sense in smallworldcoupled interacting systems where relaxation is the relevant nodetonode process and effectively governs the dynamics. We also show that the statistics of the extreme fluctuations is given by the FisherTippet Type I (Gumbel) distribution. We demonstrate our results on an actual synchronizational problem in the context of scalable parallel computing(G. Korniss, M.A. Novotny, H. Guclu, Z. Toroczkai, and P.A. Rikvold, Science 299), 677 (2003)..
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MARY18007G