Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 172608, 11 pages
http://dx.doi.org/10.1155/2013/172608
Research Article

Synchronization of Complex Dynamical Networks with Nonidentical Nodes and Derivative Coupling via Distributed Adaptive Control

Department of Mathematics, Xidian University, Xi’an 710071, China

Received 23 May 2013; Revised 19 August 2013; Accepted 19 August 2013

Academic Editor: Jun Hu

Copyright © 2013 Miao Shi 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, “Exploring complex networks,” Nature, vol. 410, no. 6825, pp. 268–276, 2001. View at Publisher · View at Google Scholar · View at Scopus
  2. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “Complex networks: structure and dynamics,” Physics Reports, vol. 424, no. 4-5, pp. 175–308, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  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 · View at Scopus
  4. D. H. Ji, S. C. Jeong, J. H. Park, S. M. Lee, and S. C. Won, “Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 4872–4880, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. X.-Y. Guo and J.-M. Li, “Stochastic synchronization for time-varying complex dynamical networks,” Chinese Physics B, vol. 21, no. 2, Article ID 020501, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Hu, Z. D. Wang, H. J. Gao, and L. K. Stergioulas, “Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 3008–3015, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. G.-P. Jiang, W. K.-S. Tang, and G. Chen, “A state-observer-based approach for synchronization in complex dynamical networks,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 12, pp. 2739–2745, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. K. Wang, X. Fu, and K. Li, “Cluster synchronization in community networks with nonidentical nodes,” Chaos, vol. 19, no. 2, Article ID 023106, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. N. Chopra and M. W. Spong, “Output synchronization of nonlinear systems with time delay in communication,” in Proceedings of the 45th IEEE Conference on Decision and Control (CDC '06), pp. 4986–4992, December 2006. View at Scopus
  10. S. Jie, E. M. Bollt, and T. Nishikawa, “Constructing generalized synchronization manifolds by manifold equation,” SIAM Journal on Applied Dynamical Systems, vol. 8, no. 1, pp. 202–221, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. Xiang and G. Chen, “On the V-stability of complex dynamical networks,” Automatica, vol. 43, no. 6, pp. 1049–1057, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. J. G. B. Ramirez and R. Femat, “On the controlled synchronization of dynamical networks with nonidentical nodes,” in Proceedings of the 3rd International IEEE Scientific Conference on Physics and Control, pp. 1253–1257, 2007.
  13. J. Zhao, D. J. Hill, and T. Liu, “Synchronization of dynamical networks with nonidentical nodes: criteria and control,” IEEE Transactions on Circuits and Systems I, vol. 58, no. 3, pp. 584–594, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. T. F. Wang, J. M. Li, and S. Tang, “Adaptive synchronization of nonlinearly parameterized complex dynamical networks with unknown time-varying parameters,” Mathematical Problems in Engineering, vol. 2012, Article ID 592539, 16 pages, 2012. View at Publisher · View at Google Scholar
  15. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, Mass, USA, 1993. View at MathSciNet
  16. S.-I. Niculescu, Delay Effects on Stability: A Robust Control Approach, Springer, Berlin, Germany, 2001. View at MathSciNet
  17. D. W. Gong, H. G. Zhang, Z. S. Wang, and B. Huang, “New global synchronization analysis for complex networks with coupling delay based on a useful inequality,” Neural Computing and Applications, vol. 22, no. 2, pp. 205–210, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. H. Xu, W. N. Zhou, J. A. Fang, and W. Sun, “Adaptive synchronization of the complex dynamical network with non-derivative and derivative coupling,” Physics Letters A, vol. 374, no. 15-16, pp. 1673–1677, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. J. Wang, L. Feng, and S.-K. Li, “Adaptive synchronization between two delayed complex networks with derivative coupling and non-identical nodes,” in Proceedings of the International Conference on Information and Automation (ICIA '11), pp. 135–140, June 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. Z. Jia, X. C. Fu, G. M. Deng, and K. Z. Li, “Group synchronization in complex dynamical networks with different types of oscillators and adaptive coupling schemes,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 10, pp. 2752–2760, 2013. View at Google Scholar
  21. J. Xiao, Y. H. Yang, and J. S. Long, “Synchronisation of complex networks with derivative coupling via adaptive control,” International Journal of Systems Science, vol. 44, no. 12, pp. 2183–2189, 2013. View at Google Scholar
  22. J. Hu, Z. D. Wang, H. J. Gao, and L. K. Stergioulas, “Robust H sliding mode control for discrete time-delay systems with stochastic nonlinearities,” Journal of the Franklin Institute, vol. 349, no. 4, pp. 1459–1479, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. J. Hu, Z. D. Wang, Y. G. Niu, and L. K. Stergioulas, “H sliding mode observer design for a class of nonlinear discrete time-delay systems: a delay-fractioning approach,” International Journal of Robust and Nonlinear Control, vol. 22, no. 16, pp. 1806–1826, 2012. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Hu, Z. D. Wang, and H. J. Gao, “A delay fractioning approach to robust sliding mode control for discrete-time stochastic systems with randomly occurring non-linearities,” IMA Journal of Mathematical Control and Information, vol. 28, no. 3, pp. 345–363, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. J.-X. Xu and Y. Tan, “A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties,” IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1940–1945, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. 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 · View at MathSciNet · View at Scopus
  27. Z. S. Wang and H. G. Zhang, “Synchronization stability in complex interconnected neural networks with nonsymmetric coupling,” Neurocomputing, vol. 108, pp. 84–92, 2013. View at Google Scholar
  28. W. Lin and C. J. Qian, “Adaptive control of nonlinearly parameterized systems: the smooth feedback case,” IEEE Transactions on Automatic Control, vol. 47, no. 8, pp. 1249–1266, 2002. View at Publisher · View at Google Scholar · View at Scopus