Extreme fluctuations in small-world networks with relaxational dynamics

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Guclu H. , Korniss G.

PHYSICAL REVIEW E, vol.69, no.6, 2004 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 6
  • Publication Date: 2004
  • Doi Number: 10.1103/physreve.69.065104
  • Title of Journal : PHYSICAL REVIEW E


We study the distribution and scaling of the extreme height fluctuations for Edwards-Wilkinson-type relaxation on small-world substrates. When random links are added to a one-dimensional lattice, the average size of the fluctuations becomes finite (synchronized state) and the extreme height diverges only logarithmically in the large system-size limit. This latter property ensures synchronization in a practical sense in small-world coupled multi-component autonomous systems. The statistics of the extreme heights is governed by the Fisher-Tippett-Gumbel distribution.