Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014 (2014), Article ID 450193, 11 pages
http://dx.doi.org/10.1155/2014/450193
Research Article

Adaptive Impulsive Observer for Outer Synchronization of Delayed Complex Dynamical Networks with Output Coupling

School of Mathematics and Statistics, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang 310018, China

Received 19 December 2013; Accepted 31 March 2014; Published 30 April 2014

Academic Editor: Junjie Wei

Copyright © 2014 Song Zheng. 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, pp. 131–132, 1999. View at Google Scholar · View at Scopus
  2. 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
  3. W. Sun, “Random walks on generalized Koch networks,” Physica Scripta, vol. 88, Article ID 045006, 2013. View at Google Scholar
  4. M. Chavez, D.-U. Hwang, A. Amann, H. G. E. Hentschel, and S. Boccaletti, “Synchronization is enhanced in weighted complex networks,” Physical Review Letters, vol. 94, no. 21, Article ID 218701, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. C. W. Wu, Synchronization in Complex Networks of Nonlinear Dynamical Systems, World Scientific Publishing, Singapore, 2007.
  6. 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
  7. D. J. Stilwell, E. M. Bollt, and D. G. Roberson, “Sufficient conditions for fast switching synchronization in time-varying network topologies,” SIAM Journal on Applied Dynamical Systems, vol. 5, no. 1, pp. 140–156, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Sorrentino and E. Ott, “Adaptive synchronization of dynamics on evolving complex networks,” Physical Review Letters, vol. 100, no. 11, Article ID 114101, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. D. H. Ji, J. H. Park, W. J. Yoo, S. C. Won, and S. M. Lee, “Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay,” Physics Letters A, vol. 374, no. 10, pp. 1218–1227, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. T. E. Gorochowski, M. di Bernardo, and C. S. Grierson, “Evolving enhanced topologies for the synchronization of dynamical complex networks,” Physical Review E, vol. 81, no. 5, Article ID 056212, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. D. H. Ji, D. W. Lee, J. H. Koo, S. C. Won, S. M. Lee, and J. H. Park, “Synchronization of neutral complex dynamical networks with coupling time-varying delays,” Nonlinear Dynamics, vol. 65, no. 4, pp. 349–358, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. G. Wang, Z. Mu, C. Wen, and Y. Li, “A new global stability criteria for neural network with two time-varying delays,” Circuits, Systems, and Signal Processing, vol. 31, no. 1, pp. 177–187, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. T. H. Lee, J. H. Park, H. Y. Jung, S. M. Lee, and O. M. Kwon, “Synchronization of a delayed complex dynamical network with free coupling matrix,” Nonlinear Dynamics, vol. 69, no. 3, pp. 1081–1090, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. W. Sun, Y. Yang, C. Li, and Z. Liu, “Synchronization inside complex dynamical networks with double time-delays and nonlinear inner-coupling functions,” International Journal of Modern Physics B, vol. 25, no. 11, pp. 1531–1541, 2011. View at Publisher · View at Google Scholar
  15. X. F. Wang and G. Chen, “Pinning control of scale-free dynamical networks,” Physica A, vol. 310, no. 3-4, pp. 521–531, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. X. Li, X. Wang, and G. Chen, “Pinning a complex dynamical network to its equilibrium,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 51, no. 10, pp. 2074–2087, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  17. T. Chen, X. Liu, and W. Lu, “Pinning complex networks by a single controller,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 54, no. 6, pp. 1317–1326, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. S. Zheng and Q. Bi, “Synchronization analysis of complex dynamical networks with delayed and non-delayed coupling based on pinning control,” Physica Scripta, vol. 84, no. 2, Article ID 025008, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. W. Xia and J. Cao, “Pinning synchronization of delayed dynamical networks via periodically intermittent control,” Chaos, vol. 19, no. 1, Article ID 013120, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  20. S. Cai, Z. Liu, F. Xu, and J. Shen, “Periodically intermittent controlling complex dynamical networks with time-varying delays to a desired orbit,” Physics Letters A, vol. 373, no. 42, pp. 3846–3854, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. Zhou, L. Xiang, and Z. Liu, “Synchronization in complex delayed dynamical networks with impulsive effects,” Physica A, vol. 384, no. 2, pp. 684–692, 2007. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Li, J. Cao, and Z. Wang, “Robust impulsive synchronization of coupled delayed neural networks with uncertainties,” Physica A, vol. 373, pp. 261–272, 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. Dai, Y. Cai, and X. Xu, “Synchronisation analysis and impulsive control of complex networks with coupling delays,” IET Control Theory & Applications, vol. 3, no. 9, pp. 1167–1174, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  24. X. P. Han and X. L. Fu, “Impulsive control induced effects on dynamics of complex networks,” Nonlinear Dynamics, vol. 3, pp. 203–216, 2010. View at Google Scholar
  25. Q. Zhang and J. Zhao, “Projective and lag synchronization between general complex networks via impulsive control,” Nonlinear Dynamics, vol. 67, no. 4, pp. 2519–2525, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. S. Zheng, “Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling,” Nonlinear Dynamics, vol. 67, no. 4, pp. 2621–2630, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. P. Wang, J. Lü, and M. J. Ogorzalek, “Global relative parameter sensitivities of the feed-forward loops in genetic networks,” Neurocomputing, vol. 78, no. 1, pp. 155–165, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. F. Sorrentino and E. Ott, “Network synchronization of groups,” Physical Review E, vol. 76, no. 5, Article ID 056114, 10 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  29. C. P. Li, W. G. Sun, and J. Kurths, “Synchronization between two coupled complex networks,” Physical Review E, vol. 76, Article ID 046204, 2007. View at Google Scholar
  30. C. Li, C. Xu, W. Sun, J. Xu, and J. Kurths, “Outer synchronization of coupled discrete-time networks,” Chaos, vol. 19, no. 1, Article ID 013106, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  31. H. Tang, L. Chen, J.-A. Lu, and C. K. Tse, “Adaptive synchronization between two complex networks with nonidentical topological structures,” Physica A, vol. 387, no. 22, pp. 5623–5630, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. W. Sun, J. Zhang, and C. Li, “Synchronization analysis of two coupled complex networks with time delays,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 209321, 12 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. S. Zheng, “Exponential synchronization of two nonlinearly non-delayed and delayed coupled complex dynamical networks,” Physica Scripta, vol. 85, no. 1, Article ID 015003, 2012. View at Publisher · View at Google Scholar · View at Scopus
  34. W. Sun and S. Li, “Generalized outer synchronization between two uncertain dynamical networks,” Nonlinear Dynamics, 2014. View at Publisher · View at Google Scholar
  35. G. Grassi and S. Mascolo, “Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 44, no. 10, pp. 1011–1014, 1997. View at Publisher · View at Google Scholar · View at Scopus
  36. J. Alvarez-Ramirez, H. Puebla, and I. Cervantes, “Stability of observer-based chaotic communications for a class of Lur'e systems,” International Journal of Bifurcation and Chaos, vol. 12, no. 7, pp. 1605–1618, 2002. View at Publisher · View at Google Scholar · View at Scopus
  37. J. G. Lu and D. J. Hill, “Impulsive synchronization of chaotic Lur'e systems by linear static measurement feedback: an LMI approach,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 8, pp. 710–714, 2007. View at Publisher · View at Google Scholar · View at Scopus
  38. 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: Regular Papers, vol. 53, no. 12, pp. 2739–2745, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  39. C.-X. Fan, G.-P. Jiang, and F.-H. Jiang, “Synchronization between two complex dynamical networks using scalar signals under pinning control,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, no. 11, pp. 2991–2998, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  40. Z. Yang and D. Xu, “Stability analysis and design of impulsive control systems with time delay,” IEEE Transactions on Automatic Control, vol. 52, no. 8, pp. 1448–1454, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  41. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific Publishing, Teaneck, NJ, USA, 1989. View at MathSciNet