Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2011, Article ID 978612, 15 pages
http://dx.doi.org/10.1155/2011/978612
Research Article

Generalized Synchronization between Two Complex Dynamical Networks with Time-Varying Delay and Nonlinear Coupling

1Faculty of Science, Jiangsu University, Jiangsu, Zhenjiang, 212013, China
2Faculty of Mathematics and Physics, Jiangsu University of Science and Technology, Jiangsu, Zhenjiang, 212003, China

Received 30 August 2010; Revised 26 March 2011; Accepted 17 May 2011

Academic Editor: E. E. N. Macau

Copyright © 2011 Qiuxiang Bian and Hongxing Yao. 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. D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998. View at Publisher · View at Google Scholar
  2. A. L. Barabási, R. Albert, and H. Jeong, “Mean-field theory for scale-free random network,” Physica A, vol. 272, no. 1-2, pp. 173–187, 1999. View at Publisher · View at Google Scholar
  3. S. H. Strogatz, “Exploring complex networks,” Nature, vol. 410, no. 6825, pp. 268–276, 2001. View at Publisher · View at Google Scholar
  4. L. Y. Xiang, Z. Q. Chen, Z. X. Liu, and Z. Z. Yuane, “Research on the modelling, analysis and control of complex dynamical networks,” Progress in Natural Science, vol. 16, no. 13, pp. 1543–1551, 2006. View at Google Scholar
  5. T. Zhou, Z. Q. Fu, and B. H. Wang, “Epidemic dynamics on complex networks,” Progress in Natural Science, vol. 16, no. 5, pp. 452–457, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. M. C. Ho, Y. C. Hung, and C. H. Chou, “Phase and anti-phase synchronization of two chaotic systems by using active control,” Physics Letters A, vol. 296, no. 1, pp. 43–48, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. H. H. Chen, G. J. Sheu, Y. L. Lin, and C. S. Chen, “Chaos synchronization between two different chaotic systems via nonlinear feedback control,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 12, pp. 4393–4401, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J. Zhou, J. A. Lu, and J. H. Lü, “Adaptive synchronization of an uncertain complex dynamical network,” IEEE Transactions on Automatic Control, vol. 51, no. 4, pp. 652–656, 2006. View at Publisher · View at Google Scholar
  9. S. M. Cai, J. Zhou, L. Xiang, and Z. R. Liu, “Robust impulsive synchronization of complex delayed dynamical networks,” Physics Letters A, vol. 372, no. 30, pp. 4990–4995, 2008. View at Publisher · View at Google Scholar
  10. X. R. Chen and C. X. Liu, “Passive control on a unified chaotic system,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 683–687, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. L. M. Pecora and T. L. Carroll, “Master stability functions for synchronized coupled systems,” Physical Review Letters, vol. 80, no. 10, pp. 2109–2112, 1998. View at Publisher · View at Google Scholar
  12. A. Arenas, A. Díaz-Guilera, and C. J. Pérez-Vicente, “Synchronization reveals topological scales in complex networks,” Physical Review Letters, vol. 96, no. 11, Article ID 114102, 4 pages, 2006. View at Publisher · View at Google Scholar
  13. M. Sun, C. Y. Zeng, and L. X. Tian, “Projective synchronization in drive-response dynamical networks of partially linear systems with time-varying coupling delay,” Physics Letters A, vol. 372, no. 46, pp. 6904–6908, 2008. View at Publisher · View at Google Scholar
  14. S. Zheng, Q. S. Bi, and G. L. Cai, “Adaptive projective synchronization in complex networks with time-varying coupling delay,” Physics Letters A, vol. 373, no. 17, pp. 1553–1559, 2009. View at Publisher · View at Google Scholar
  15. X. Q. Yu, Q. S. Ren, J. L. Hou, and J. Y. Zhao, “The chaotic phase synchronization in adaptively coupled-delayed complex networks,” Physics Letters A, vol. 373, no. 14, pp. 1276–1282, 2009. View at Publisher · View at Google Scholar
  16. X. Li, “Phase synchronization in complex networks with decayed long-range interactions,” Physica D, vol. 223, no. 2, pp. 242–247, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. X. L. Xu, Z. Q. Chen, G. Y. Si, X. F. Hu, and P. Luo, “A novel definition of generalized synchronization on networks and a numerical simulation example,” Computers & Mathematics with Applications, vol. 56, no. 11, pp. 2789–2794, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. Y. C. Hung, Y. T. Huang, M. C. Ho, and C. K. Hu, “Paths to globally generalized synchronization in scale-free networks,” Physical Review E, vol. 77, no. 1, Article ID 016202, 8 pages, 2008. View at Publisher · View at Google Scholar
  19. J. F. Li, N. Li, Y. P. Liu, and Y. Gan, “Linear and nonlinear generalized synchronization of a class of chaotic systems by using a single driving variable,” Acta Physica Sinica, vol. 58, no. 2, pp. 779–784, 2009. View at Google Scholar · View at Zentralblatt MATH
  20. J. Zhou and J. A. Lu, “Topology identification of weighted complex dynamical networks,” Physica A, vol. 386, no. 1, pp. 481–491, 2007. View at Publisher · View at Google Scholar
  21. X. W. Liu and T. P. Chen, “Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling,” Physica A, vol. 381, no. 15, pp. 82–92, 2007. View at Publisher · View at Google Scholar
  22. G. M. He and J. Y. Yang, “Adaptive synchronization in nonlinearly coupled dynamical networks,” Chaos, Solitons and Fractals, vol. 38, no. 5, pp. 1254–1259, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. J. G. Peng, H. Qiao, and Z. B. Xu, “A new approach to stability of neural networks with time-varying delays,” Neural Networks, vol. 15, no. 1, pp. 95–103, 2002. View at Publisher · View at Google Scholar
  24. G. Tao, “A simple alternative to the Barbǎlat lemma,” IEEE Transactions on Automatic Control, vol. 42, no. 5, p. 698, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. J. H. Lü, G. R. Chen, D. Z. Cheng, and S. Celikovsky, “Bridge the gap between the Lorenz system and the Chen system,” International Journal of Bifurcation and Chaos, vol. 12, no. 12, pp. 2917–2926, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. H. K. Chen and C. I. Lee, “Anti-control of chaos in rigid body motion,” Chaos, Solitons and Fractals, vol. 21, no. 4, pp. 957–965, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH