Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 616289, 13 pages
http://dx.doi.org/10.1155/2013/616289
Research Article

Synchronization of Coupled Networks with Uncertainties

1Division of Information, Chongqing University of Science and Technology, Chongqing 401331, China
2Department of Mathematics, Chongqing Normal University, Chongqing 401331, China

Received 25 September 2013; Accepted 5 November 2013

Academic Editor: Qiankun Song

Copyright © 2013 Yi Zuo and Xinsong Yang. 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. B. A. Huberman and L. A. Adamic, “Growth dynamics of the world-wide web,” Nature, vol. 401, no. 6749, p. 131, 1999. View at Google Scholar · View at Scopus
  2. R. Pastor-Satorras, E. Smith, and R. V. Solé, “Evolving protein interaction networks through gene duplication,” Journal of Theoretical Biology, vol. 222, no. 2, pp. 199–210, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. Pastor-Satorras and A. Vespignani, “Epidemic spreading in scale-free networks,” Physical Review Letters, vol. 86, no. 14, pp. 3200–3203, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. A. L. Barabási, H. Jeong, Z. Néda, E. Ravasz, A. Schubert, and T. Vicsek, “Evolution of the social network of scientific collaborations,” Physica A, vol. 311, no. 3-4, pp. 590–614, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. F. Wang and Y. Sun, “Self-organizing peer-to-peer social networks,” Computational Intelligence, vol. 24, no. 3, pp. 213–233, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. C. Wu and L. Chua, “Synchronization in an array of linearly coupled dynamical systems,” IEEE Transactions on Circuits and Systems I, vol. 42, no. 8, pp. 430–447, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. X. Yang and J. Cao, “Stochastic synchronization of coupled neural networks with intermittent control,” Physics Letters A, vol. 373, no. 36, pp. 3259–3272, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. D. Chen, W. Zhao, X. Ma, and R. Zhang, “Control and synchronization of chaos in RCL-shunted Josephson junction with noise disturbance using only one controller term,” Abstract and Applied Analysis, vol. 2012, Article ID 378457, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. X. Yang and J. Cao, “Finite-time stochastic synchronization of complex networks,” Applied Mathematical Modelling, vol. 34, no. 11, pp. 3631–3641, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. C. Li, X. Liao, and K. Wong, “Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication,” Physica D, vol. 194, no. 3-4, pp. 187–202, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. X. Yang, S. Ai, T. Su, and A. Chang, “Synchronization of general complex networks with hybrid couplings and unknown perturbations,” Abstract and Applied Analysis, vol. 2013, Article ID 635372, 14 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Q. Xie, G. Chen, and E. Bollt, “Hybrid chaos synchronization and its application in information processing,” Mathematical and Computer Modelling, vol. 35, no. 1-2, pp. 145–163, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. W. Yu, W. Ren, W. X. Zheng, G. Chen, and J. Lü, “Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics,” Automatica, vol. 49, no. 7, pp. 2107–2115, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Cao, Z. Wang, and Y. Sun, “Synchronization in an array of linearly stochastically coupled networks with time delays,” Physica A, vol. 385, no. 2, pp. 718–728, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Chen and D. Zhou, “Synchronization in uncertain complex networks,” Chaos, vol. 16, no. 1, Article ID 013101, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. W. Guo, F. Austin, S. Chen, and W. Sun, “Pinning synchronization of the complex networks with non-delayed and delayed coupling,” Physics Letters A, vol. 373, no. 17, pp. 1565–1572, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. W. Yu, P. DeLellis, G. Chen, M. di Bernardo, and J. Kurths, “Distributed adaptive control of synchronization in complex networks,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2153–2158, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Y. Liu, Z. Wang, and X. Liu, “Exponential synchronization of complex networks with Markovian jump and mixed delays,” Physics Letters A, vol. 372, no. 22, pp. 3986–3998, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. X. Yang and J. Cao, “Adaptive pinning synchronization of complex networks with stochastic perturbations,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 416182, 21 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. J. Zhou, J. Lu, and J. 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
  21. J. Zhou, J. Lu, and J. Lü, “Pinning adaptive synchronization of a general complex dynamical network,” Automatica, vol. 44, no. 4, pp. 996–1003, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. J. Zhou, X. Wu, W. Yu, M. Small, and J. Lu, “Pinning synchronization of delayed neural networks,” Chaos, vol. 18, no. 4, Article ID 043111, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. C. W. Park, C. H. Lee, and M. Park, “Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty,” Information Sciences, vol. 147, no. 1–4, pp. 245–266, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. S. Bowong and F. Kakmeni, “Chaos control and duration time of a class of uncertain chaotic systems,” Physics Letters A, vol. 316, no. 3-4, pp. 206–217, 2003. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Huang and G. Feng, “Synchronization of nonidentical chaotic neural networks with time delays,” Neural Networks, vol. 22, no. 7, pp. 869–874, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. R. N. Madan, Chua’s Circuit: A Paradigm for Chaos, vol. 1, World Scientific, Singapore, 1993. View at MathSciNet
  27. E. N. Lorenz, “Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, pp. 130–141, 1963. View at Google Scholar
  28. O. E. Rössler, “An equation for continuous chaos,” Physics Letters A, vol. 57, no. 5, pp. 397–398, 1976. View at Publisher · View at Google Scholar
  29. G. Chen and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and Chaos, vol. 9, no. 7, pp. 1465–1466, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  30. H. Huijberts, H. Nijmeijer, and T. Oguchi, “Anticipating synchronization of chaotic Lur’e systems,” Chaos, vol. 17, no. 1, Article ID 013117, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. X. Wang, G. Zhong, K. Tang, K. Man, and Z. Liu, “Generating chaos in Chua's circuit via time-delay feedback,” IEEE Transactions on Circuits and Systems I, vol. 48, no. 9, pp. 1151–1156, 2001. View at Publisher · View at Google Scholar · View at Scopus
  32. E. B. Kosmatopoulos, M. M. Polycarpou, M. A. Christodoulou, and P. A. Ioannou, “High-order neural network structures for identification of dynamical systems,” IEEE Transactions on Neural Networks, vol. 6, no. 2, pp. 422–431, 1995. View at Publisher · View at Google Scholar · View at Scopus
  33. J. J. Rubio, “SOFMLS: online self-organizing fuzzy modified least-squares network,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 6, pp. 1296–1309, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. W. Yu and J. J. Rubio, “Recurrent neural networks training with stable bounding ellipsoid algorithm,” IEEE Transactions on Neural Networks, vol. 20, no. 6, pp. 983–991, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. V. Popov, Hyperstability of Control System, vol. 204 of Grundlehren der mathematischen Wissenschaften, Springer, Berlin, Germany, 1973.
  36. C. Edwards, S. Spurgeon, and R. Patton, “Sliding mode observers for fault detection and isolation,” Automatica, vol. 36, no. 4, pp. 541–553, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  37. J. Lin and J. Yan, “Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller,” Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 1151–1159, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  38. Y. Tang, J. Fang, and Q. Miao, “On the exponential synchronization of stochastic jumping chaotic neural networks with mixed delays and sector-bounded non-linearities,” Neurocomputing, vol. 72, no. 7-9, pp. 1694–1701, 2009. View at Publisher · View at Google Scholar · View at Scopus
  39. D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998. View at Google Scholar · View at Scopus