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Mathematical Problems in Engineering
Volume 2013, Article ID 451960, 7 pages
http://dx.doi.org/10.1155/2013/451960
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.

Linked References

  1. S. H. Strogatz and I. Stewart, “Coupled oscillators and biological synchronization,” Scientific American, vol. 269, no. 6, pp. 102–109, 1993. View at Google Scholar · View at Scopus
  2. C. M. Gray, “Synchronous oscillations in neuronal systems: mechanisms and functions,” Journal of Computational Neuroscience, vol. 1, no. 1-2, pp. 11–38, 1994. View at Publisher · View at Google Scholar · View at Scopus
  3. L. Glass, “Synchronization and rhythmic processes in physiology,” Nature, vol. 410, no. 6825, pp. 277–284, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. M. S. de Vieira, “Chaos and synchronized chaos in an earthquake model,” Physical Review Letters, vol. 82, no. 1, pp. 201–204, 1999. View at Google Scholar · View at Scopus
  5. S. H. Wang, J. Y. Kuang, J. H. Li, Y. L. Luo, H. P. Lu, and G. Hu, “Chaos-based secure communications in a large community,” Physical Review E, vol. 66, no. 6, Article ID 065202, 2002. View at Google Scholar
  6. D. Yu, M. Righero, and L. Kocarev, “Estimating topology of networks,” Physical Review Letters, vol. 97, no. 18, Article ID 188701, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Milgram, “The small world problem,” in Psychology Today, vol. 2, pp. 60–67, Sussex Publishers, 1967. View at Google Scholar
  8. D. J. Watts and S. H. Strogatz, “Collective dynamics of small-world networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998. View at Google Scholar · View at Scopus
  9. M. E. J. Newman and D. J. Watts, “Renormalization group analysis of the small-world network model,” Physics Letters A, vol. 263, no. 4–6, pp. 341–346, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. F. Wang and G. Chen, “Synchronization in small-world dynamical networks,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 1, pp. 187–192, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. F. Qi, Z. Hou, and H. Xin, “Ordering chaos by random shortcuts,” Physical Review Letters, vol. 91, no. 6, Article ID 064102, 2003. View at Google Scholar · View at Scopus
  12. V. N. Belykh, I. V. Belykh, and M. Hasler, “Connection graph stability method for synchronized coupled chaotic systems,” Physica D, vol. 195, no. 1-2, pp. 159–187, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. I. V. Belykh, V. N. Belykh, and M. Hasler, “Blinking model and synchronization in small-world networks with a time-varying coupling,” Physica D, vol. 195, no. 1-2, pp. 188–206, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. L. Tang, J. Lu, and G. Chen, “Synchronizability of small-world networks generated from ring networks with equal-distance edge additions,” Chaos, vol. 22, no. 2, Article ID 023121. View at Publisher · View at Google Scholar
  15. T. Nishikawa, A. E. Motter, Y.-C. Lai, and F. C. Hoppensteadt, “Heterogeneity in oscillator networks: are smaller worlds easier to synchronize?” Physical Review Letters, vol. 91, no. 1, Article ID 014101, 2003. View at Google Scholar · View at Scopus
  16. M. Zhao, T. Zhou, B.-H. Wang, G. Yan, H.-J. Yang, and W.-J. Bai, “Relations between average distance, heterogeneity and network synchronizability,” Physica A, vol. 371, no. 2, pp. 773–780, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. X. F. Wang, X. Li, and G. Chen, Complex Network and Application, Tsinghua University Press, Beijing, China, 2006.
  18. X. F. Wang, X. Li, and G. Chen, Network Science: An Introduction, Higher Education Press, Beijing, China, 2012.
  19. J. Kleinberg, “The small-world phenomenon: an algorithm perspective,” in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  20. Y. Zhao, J. W. Feng, and J. Y. Wang, “On synchronizability of kleinberg small world networks,” in Proceedings of 8th International Conference on Computational Intelligence and Security, pp. 204–208, 2012.
  21. T. Nishikawa and A. E. Motter, “Maximum performance at minimum cost in network synchronization,” Physica D, vol. 224, no. 1-2, pp. 77–89, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet