About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 946243, 8 pages
http://dx.doi.org/10.1155/2013/946243
Research Article

Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes

College of Mathematics and Computational Sciences, Shenzhen University, Shenzhen, Guangdong 518060, China

Received 5 August 2012; Revised 21 November 2012; Accepted 18 December 2012

Academic Editor: Shukai Duan

Copyright © 2013 Ze Tang and Jianwen Feng. 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 and I. Stewart, “Coupled oscillators and biological synchronization,” Scientific American, vol. 269, no. 6, pp. 102–109, 1993. View at Publisher · View at Google Scholar
  2. C. M. Gray, “Synchronous oscillations in neural systems,” Journal of Computational Neuroscience, vol. 1, no. 1-2, pp. 11–38, 1994. View at Publisher · View at Google Scholar
  3. J. Fell and N. Axmacher, “The role of phase synchronization in memory processes,” Nature Reviews Neuroscience, vol. 12, no. 2, pp. 105–118, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. W. He, F. Qian, J. Cao, and Q. L. Han, “Impulsive synchronization of two nonidentical chaotic systems with time-varying delay,” Physics Letters A, vol. 375, no. 3, pp. 498–504, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Y. Li, B. Chen, Q. Zhou, and W. Y. Qian, “Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 39, no. 1, pp. 94–102, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. H. Y. Li, H. J. Gao, and P. Shi, “New passivity analysis for neural networks with discrete and distributed delays,” IEEE Transactions on Neural Networks, vol. 21, no. 11, pp. 1842–1847, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, vol. 12 of Cambridge Nonlinear Science Series, Cambridge University Press, Cambridge, UK, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  9. Y. Tang, H. Gao, W. Zou, and J. Kurths, “Identifying controlling nodes in neuronal networks in different scales,” PLoS ONE, vol. 7, Article ID e41375, 2012.
  10. J. Y. Wang, J. W. 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
  11. W. Wu, W. J. Zhou, and T. P. Chen, “Cluster synchronization of linearly coupled complex networks under pinning control,” IEEE Transactions on Circuits and Systems I, vol. 56, no. 4, pp. 829–839, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. K. H. Wang, X. C. Fu, and K. Z. Li, “Cluster synchronization in community networks with nonidentical nodes,” Chaos, vol. 19, no. 2, Article ID 023106, 10 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. D. Cao and L. L. Li, “Cluster synchronization in an array of hybrid coupled neural networks with delay,” Neural Networks Letter, vol. 47, no. 11, pp. 2395–2405, 2011.
  14. W. B. Zhang, Y. Tang, J. A. Fang, and W. Zhu, “Exponential cluster synchronization of impulsive delayed genetic oscillators with external disturbances,” Chaos, vol. 21, no. 4, Article ID 043137, 2011. View at Publisher · View at Google Scholar
  15. J. Q. Lu and J. D. Cao, “Adaptive synchronization of uncertain dynamical networks with delayed coupling,” Nonlinear Dynamics, vol. 53, no. 1-2, pp. 107–115, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. W. L. He and J. D. Cao, “Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters,” Physics Letters A, vol. 372, no. 4, pp. 408–416, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. H. Sun and J. D. Cao, “Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation,” Physics Letters A, vol. 364, no. 3-4, pp. 277–285, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. W. W Yu and J. D. Cao, “Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification,” Physica A, vol. 375, no. 2, pp. 467–482, 2007. View at Publisher · View at Google Scholar · View at Scopus
  19. J. Q. Lu and J. D. 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. Y. Y. Wu, C. P. Li, A. L. Yang, L. J. Song, and Y. J. Wu, “Pinning adaptive anti-synchronization between two general complex dynamical networks with non-delayed and delayed coupling,” Applied Mathematics and Computation, vol. 218, no. 14, pp. 7445–7452, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. D. G. Xu and Z. F. Su, “Synchronization criterions and pinning control of general complex networks with time delay,” Applied Mathematics and Computation, vol. 215, no. 4, pp. 1593–1608, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. K. Lou, B. T. Cui, and X. J. Zhang, “Adaptive synchronization of two complex networks with delayed and non-delayed coupling,” Arabian Journal of Mathematics, vol. 1, no. 2, pp. 219–226, 2012. View at Publisher · View at Google Scholar
  23. X. J. Wu and H. T. Lu, “Exponential synchronization of weighted general delay coupled and non-delay coupled dynamical networks,” Computers and Mathematics with Applications, vol. 60, no. 8, pp. 2476–2487, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. W. L. Lu and T. P. Chen, “New approach to synchronization analysis of linearly coupled ordinary differential systems,” Physica D, vol. 213, no. 2, pp. 214–230, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, “Delay-dependent robust stabilization of uncertain state-delayed systems,” International Journal of Control, vol. 74, no. 14, pp. 1447–1455, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet