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Mathematical Problems in Engineering
Volume 2013, Article ID 451960, 7 pages
Research Article

Synchronizability of Small-World Networks Generated from a Two-Dimensional Kleinberg Model

1College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, China
2College of Information and Engineering, Shenzhen University, Shenzhen 518060, China

Received 5 June 2013; Accepted 26 July 2013

Academic Editor: Wenwu Yu

Copyright © 2013 Yi Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper investigates the synchronizability of small-world networks generated from a two-dimensional Kleinberg model, which is more general than NW small-world network. The three parameters of the Kleinberg model, namely, the distance of neighbors, the number of edge-adding, and the edge-adding probability, are analyzed for their impacts on its synchronizability and average path length. It can be deduced that the synchronizability becomes stronger as the edge-adding probability increases, and the increasing edge-adding probability could make the average path length of the Kleinberg small-world network go smaller. Moreover, larger distance among neighbors and more edges to be added could play positive roles in enhancing the synchronizability of the Kleinberg model. The lorentz oscillators are employed to verify the conclusions numerically.