Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 287670, 19 pages
http://dx.doi.org/10.1155/2011/287670
Research Article

Global Synchronization of Complex Networks with Discrete Time Delays on Time Scales

Department of Mathematics, Southeast University, Nanjing 210096, China

Received 4 April 2011; Accepted 9 June 2011

Academic Editor: Wei-Der Chang

Copyright © 2011 Quanxin Cheng and Jinde Cao. 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. J. Cao, D. W. C. Ho, and X. Huang, “LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 7, pp. 1558–1572, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. Liang, J. Cao, and D. W. C. Ho, “Discrete-time bidirectional associative memory neural networks with variable delays,” Physics Letters A, vol. 335, no. 2-3, pp. 226–234, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. S. H. Strogatz, “Exploring complex networks,” Nature, vol. 410, no. 6825, pp. 268–276, 2001. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  4. X. Nie and J. Cao, “Stability analysis for the generalized Cohen-Grossberg neural networks with inverse Lipschitz neuron activations,” Computers & Mathematics with Applications, vol. 57, no. 9, pp. 1522–1536, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Z. Wang, Y. Liu, M. Li, and X. Liu, “Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 17, no. 3, pp. 814–820, 2006. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  6. Z. Wang, H. Shu, J. Fang, and X. Liu, “Robust stability for stochastic Hopfield neural networks with time delays,” Nonlinear Analysis: Real World Applications, vol. 7, no. 5, pp. 1119–1128, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C. Li and G. Chen, “Synchronization in general complex dynamical networks with coupling delays,” Physica A, vol. 343, no. 1–4, pp. 263–278, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. Cao, H. X. Li, and D. W. C. Ho, “Synchronization criteria of Lur'e systems with time-delay feedback control,” Chaos, Solitons & Fractals, vol. 23, no. 4, pp. 1285–1298, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. Cao, P. Li, and W. Wang, “Global synchronization in arrays of delayed neural networks with constant and delayed coupling,” Physics Letters A, vol. 353, no. 4, pp. 318–325, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. W. Lu and T. Chen, “Synchronization analysis of linearly coupled networks of discrete time systems,” Physica D, vol. 198, no. 1-2, pp. 148–168, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Qiu and J. Cao, “Global synchronization of delay-coupled genetic oscillators,” Neurocomputing, vol. 72, no. 16–18, pp. 3845–3850, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. 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
  13. J. Liang, Z. Wang, Y. Liu, and X. Liu, “Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 38, no. 4, pp. 1073–1083, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  14. J. Lü, X. Yu, and G. Chen, “Chaos synchronization of general complex dynamical networks,” Physica A, vol. 334, no. 1-2, pp. 281–302, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  15. G. Chen, J. Zhou, and Z. Liu, “Global synchronization of coupled delayed neural networks and applications to chaotic CNN models,” International Journal of Bifurcation and Chaos, vol. 14, no. 7, pp. 2229–2240, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. Cao and J. Lu, “Adaptive synchronization of neural networks with or without time-varying delay,” Chaos, vol. 16, no. 1, Article ID 013133, 6 pages, 2006. View at Publisher · View at Google Scholar · View at PubMed · View at Zentralblatt MATH · View at MathSciNet
  17. J. Cao, G. Chen, and P. Li, “Global synchronization in an array of delayed neural networks with hybrid coupling,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 38, no. 2, pp. 488–498, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  18. J. Liang and J. Cao, “Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays,” Physics Letters A, vol. 314, no. 5-6, pp. 434–442, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. J. Lu and J. Cao, “Adaptive synchronization in tree-like dynamical networks,” Nonlinear Analysis: Real World Applications, vol. 8, no. 4, pp. 1252–1260, 2007. 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 Scopus
  21. D. Yue and H. Li, “Synchronization stability of continuous/discrete complex dynamical networks with interval time-varying delays,” Neurocomputing, vol. 73, no. 4–6, pp. 809–819, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. H. Xu, Y. Chen, and K. L. Teo, “Global exponential stability of impulsive discrete-time neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 537–544, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001.
  24. R. Agarwal, M. Bohner, D. O'Regan, and A. Peterson, “Dynamic equations on time scales: a survey,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 1–26, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. Bohner, A. Peterson, and D. O'Regan, Eds., Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003.
  26. A. Chen and D. Du, “Global exponential stability of delayed BAM network on time scale,” Neurocomputing, vol. 71, no. 16–18, pp. 3582–3588, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. A. Chen and F. Chen, “Periodic solution to BAM neural network with delays on time scales,” Neurocomputing, vol. 73, no. 1–3, pp. 274–282, 2009. View at Publisher · View at Google Scholar
  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.
  29. A. N. Langville and W. J. Stewart, “The Kronecker product and stochastic automata networks,” Journal of Computational and Applied Mathematics, vol. 167, no. 2, pp. 429–447, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. Q. Cheng and J. Cao, “Global synchronization of complex networks with discrete time delays and stochastic disturbances,” Neural Computing & Applications. In press. View at Publisher · View at Google Scholar