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The European Physical Journal B

, Volume 63, Issue 4, pp 515–520 | Cite as

Consensus on de Bruijn graphs

  • G. Yan
  • Z. -Q. Fu
  • G. Chen
Article

Abstract

We study the consensus dynamics with or without time-delays on directed and undirected de Bruijn graphs. Our results show that consensus on an undirected de Bruijn graph has a lower converging speed and larger time-delay tolerance in comparison with that on an undirected scale-free network. Although there is not much difference between the eigenvalue ratios of the two undirected networks, we found that their dynamical properties are remarkably different; consequently, it is seemingly more informative to consider the second smallest and the largest eigenvalues separately rather than considering their ratio in the study of synchronization of a coupled oscillators network. Moreover, our study on directed de Bruijn graphs reveals that properly setting directions on edges can improve the converging speed and time-delay tolerance simultaneously.

PACS

89.75.-k Complex systems 05.45.Xt Synchronization; coupled oscillators 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Electronic Science and TechnologyUniversity of Science and Technology of ChinaHefeiP.R. China
  2. 2.Centre for Chaos and Complex Networks and Department of Electronic EngineeringCity University of Hong KongHong Kong SARP.R. China

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