About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 914140, 10 pages
http://dx.doi.org/10.1155/2013/914140
Research Article

Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

1Department of Mathematics and Finance, Yunyang Teachers’ College, Hubei 442000, China
2College of Information Science and Technology, Donghua University, Shanghai 201620, China

Received 7 March 2013; Revised 3 August 2013; Accepted 7 August 2013

Academic Editor: Sarangapani Jagannathan

Copyright © 2013 Chengrong Xie 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. X. F. Wang and G. Chen, “Synchronization in scale-free dynamical networks: robustness and fragility,” IEEE Transactions on Circuits and Systems I, vol. 49, no. 1, pp. 54–62, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  2. X. Li and G. Chen, “Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint,” IEEE Transactions on Circuits and Systems I, vol. 50, no. 11, pp. 1381–1390, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J. Lü and G. Chen, “A time-varying complex dynamical network model and its controlled synchronization criteria,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 841–846, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. Lü, X. Yu, G. Chen, and D. Cheng, “Characterizing the synchronizability of small-world dynamical networks,” IEEE Transactions on Circuits and Systems I, vol. 51, no. 4, pp. 787–796, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  5. W. Yu and J. Cao, “Synchronization control of stochastic delayed neural networks,” Physica A, vol. 373, pp. 252–260, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. W. Yu, G. Chen, and J. Cao, “Adaptive synchronization of uncertain coupled stochastic complex networks,” Asian Journal of Control, vol. 13, no. 3, pp. 418–429, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. X. Yang, J. Cao, and J. Lu, “Synchronization of delayed complex dynamical networks with impulsive and stochastic effects,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 2252–2266, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Cao and L. Li, “Cluster synchronization in an array of hybrid coupled neural networks with delay,” Neural Networks, vol. 22, no. 4, pp. 335–342, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. W. Yu and J. Cao, “Robust control of uncertain stochastic recurrent neural networks with time-varying delay,” Neural Processing Letters, vol. 26, no. 2, pp. 101–119, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. Tang, J. Fang, M. Xia, and X. Gu, “Synchronization of Takagi-Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays,” Applied Mathematical Modelling, vol. 34, no. 4, pp. 843–855, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Z.-G. Wu, P. Shi, H. Su, and J. Chu, “Passivity analysis for discrete-time stochastic markovian jump neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 22, no. 10, pp. 1566–1575, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. Wu, P. Shi, H. Su, and J. Chu, “Dissipativity analysis for discrete-time stochastic neural networks with time-varying delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, pp. 345–3355, 2013.
  13. S. Zheng, S. Wang, G. Dong, and Q. Bi, “Adaptive synchronization of two nonlinearly coupled complex dynamical networks with delayed coupling,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 284–291, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. Xu, S. Jagannathan, and F. L. Lewis, “Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses,” Automatica, vol. 48, no. 6, pp. 1017–1030, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. X. Liu and T. Chen, “Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling,” Physica A, vol. 381, no. 1-2, pp. 82–92, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Shen, Z. Wang, and Y. S. Hung, “Distributed H-consensus filtering in sensor networks with multiple missing measurements: the finite-horizon case,” Automatica, vol. 46, no. 10, pp. 1682–1688, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Y. Tang, R. Qiu, J. Fang, Q. Miao, and M. Xia, “Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays,” Physics Letters A, vol. 372, no. 24, pp. 4425–4433, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. H. Peng, N. Wei, L. Li, W. Xie, and Y. Yang, “Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control,” Physics Letters A, vol. 374, no. 23, pp. 2335–2339, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. B. Shen, Z. Wang, H. Shu, and G. Wei, “Robust H finite-horizon filtering with randomly occurred nonlinearities and quantization effects,” Automatica, vol. 46, no. 11, pp. 1743–1751, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. Lu, D. W. C. Ho, and J. Cao, “A unified synchronization criterion for impulsive dynamical networks,” Automatica, vol. 46, no. 7, pp. 1215–1221, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. Lu, J. Kurths, and J. Cao, “Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 2, pp. 285–292, 2012.
  22. J. Lu, D. W. C. Ho, J. Cao, and J. Kurths, “Single impulsive controller for globally exponential synchronization of dynamical networks,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 581–593, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. J. Lu and D. W. C. Ho, “Stabilization of complex dynamical networks with noise disturbance under performance constraint,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 1974–1984, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J. Lu, D. W. C. Ho, J. Cao, and J. Kurths, “Exponential synchronization of linearly coupled neural networks with impulsive disturbances,” IEEE Transactions on Neural Networks, vol. 22, no. 2, pp. 329–335, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. Xu, H. Yang, D. Tong, and Y. Wang, “Adaptive exponential synchronization in pth moment for stochastic time varying multi-delayed complex networks,” Nonlinear Dynamics, vol. 73, no. 3, pp. 1423–1431, 2013. View at Publisher · View at Google Scholar
  26. J. Zhou, L. Xiang, and Z. Liu, “Synchronization in complex delayed dynamical networks with impulsive effects,” Physica A, vol. 384, no. 2, pp. 684–692, 2007. View at Publisher · View at Google Scholar · View at Scopus
  27. Y. Xu, W. Zhou, J. Fang, and W. Sun, “Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 3337–3343, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  29. X. Mao, “A note on the LaSalle-type theorems for stochastic differential delay equations,” Journal of Mathematical Analysis and Applications, vol. 268, no. 1, pp. 125–142, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. J. Lü and G. Chen, “A new chaotic attractor coined,” International Journal of Bifurcation and Chaos, vol. 12, no. 3, pp. 659–661, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet