Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2014, Article ID 835867, 9 pages
http://dx.doi.org/10.1155/2014/835867
Research Article

Cluster Synchronization of Stochastic Complex Networks with Markovian Switching and Time-Varying Delay via Impulsive Pinning Control

Industrial Training Center, Shenzhen Polytechnic, Shenzhen 518000, China

Received 4 April 2014; Revised 4 June 2014; Accepted 4 June 2014; Published 26 June 2014

Academic Editor: Luca Guerrini

Copyright © 2014 Xuan Zhou and Kui Luo. 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. L. A. N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley, “Classes of small-world networks,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, pp. 11149–11152, 2000. View at Publisher · View at Google Scholar
  2. A. Zheleznyak and L. O. Chua, “coexistence of low- and high-dimensional spatiotemporal chaos in a chain of dissipatively coupled chua’s circuits,” International Journal of Bifurcation and Chaos, vol. 4, pp. 639–674, 1994. View at Publisher · View at Google Scholar
  3. M. Faloutsos, P. Faloutsos, and C. Faioutsos, “On power-law relationships of the internet topology,” in Proceedings of the ACM SIGCOMM Conference Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 251–261, September 1999. View at Scopus
  4. A. Medina, I. Matt, and J. Byers, “On the origin of power laws in internet topologies,” Computer Communication Review, vol. 30, pp. 18–28, 2000. View at Publisher · View at Google Scholar
  5. A. Perez-Munuzuri, V. Perez-Munuzuri, V. Perez-Villar, and L. O. Chua, “Synchronization in an array of linearly coupled dynamical systems,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 42, no. 8, pp. 430–447, 1995. View at Publisher · View at Google Scholar
  6. R. Albert, H. Jeong, and A. L. Barabási, “Diameter of the world-wide web,” Nature, vol. 401, no. 6749, pp. 130–131, 1999. View at Publisher · View at Google Scholar · View at Scopus
  7. S. H. Wang, J. Y. Kuang, J. H. Li, and Y. L. Luo, “Chaos-based secure communications in a large community,” Physical Review E, vol. 66, Article ID 065202, 2002. View at Publisher · View at Google Scholar
  8. B. Rakshit, A. R. Chowdhury, and P. Saha, “Parameter estimation of a delay dynamical system using synchronization in presence of noise,” Chaos, Solitons and Fractals, vol. 32, no. 4, pp. 1278–1284, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. Z. G. Zheng and G. Hu, “Generalized synchronization versus phase synchronization,” Physical Review E, vol. 62, article 7882, 2000. View at Publisher · View at Google Scholar
  10. M. G. Earl and S. H. Strogatz, “Synchronization in oscillator networks with delayed coupling: A stability criterion,” Physical Review E, vol. 67, no. 3, Article ID 036204, 2003. View at Google Scholar · View at Scopus
  11. E. G. de Oliveira and T. Braun, “Partial synchronization on a network with different classes of oscillators,” Physical Review E, vol. 76, Article ID 067201, 2007. View at Publisher · View at Google Scholar
  12. K. Wang, X. Fu, and K. Li, “Cluster synchronization in community networks with nonidentical nodes,” Chaos. An Interdisciplinary Journal of Nonlinear Science, vol. 19, no. 2, Article ID 023106, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  13. K. Kaneko, “Relevance of dynamic clustering to biological networks,” Physica D: Nonlinear Phenomena, vol. 75, no. 1–3, pp. 55–73, 1994. View at Google Scholar · View at Scopus
  14. I. Belykh, V. Belykh, K. Nevidin, and M. Hasler, “Persistent clusters in lattices of coupled nonidentical chaotic systems,” Chaos, vol. 13, no. 1, pp. 165–178, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. Pogromsky, G. Santoboni, and H. Nijmeijer, “Partial synchronization: from symmetry towards stability,” Physica D, vol. 172, no. 1–4, pp. 65–87, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z. Ma, Z. Liu, and G. Zhang, “A new method to realize cluster synchronization in connected chaotic networks,” Chaos, vol. 16, no. 2, Article ID 023103, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Y. Sun, J. Cao, and Z. Wang, “Exponential synchronization of stochastic perturbed chaotic delayed neural networks,” Neurocomputing, vol. 70, no. 13–15, pp. 2465–2477, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. J. Cao, Z. Wang, and Y. Sun, “Synchronization in an array of linearly stochastically coupled networks with time delays,” Physica A, vol. 385, no. 2, pp. 718–728, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  19. X. Yang and J. Cao, “Stochastic synchronization of coupled neural networks with intermittent control,” Physics Letters A, vol. 373, no. 36, pp. 3259–3272, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. 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
  21. J. Wang, C. Xu, J. Feng, M. K. Kwong, and F. Austin, “Mean-square exponential synchronization of markovian switching stochastic complex networks with time-varying delays by pinning control,” Abstract and Applied Analysis, vol. 2012, Article ID 298095, 2012. View at Publisher · View at Google Scholar
  22. Y. Tang and J.-a. Fang, “Adaptive synchronization in an array of chaotic neural networks with mixed delays and jumping stochastically hybrid coupling,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 9-10, pp. 3615–3628, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. W. Wu, W. Zhou, and T. Chen, “Cluster synchronization of linearly coupled complex networks under pinning control,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 56, no. 4, pp. 829–839, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  24. J. Wang, J. Feng, C. Xu, and Y. Zhao, “Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix,” Nonlinear Dynamics, vol. 67, no. 2, pp. 1635–1646, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. J. Wang, J. Feng, C. Xu, and Y. Zhao, “Exponential synchronization of stochastic perturbed complex networks with time-varying delays via periodically intermittent pinning,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 11, pp. 3146–3157, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  26. C. Yuan and X. Mao, “Robust stability and controllability of stochastic differential delay equations with Markovian switching,” Automatica, vol. 40, no. 3, pp. 343–354, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet