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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 965297, 8 pages
http://dx.doi.org/10.1155/2014/965297
Research Article

Complex Projective Synchronization in Drive-Response Stochastic Complex Networks by Impulsive Pinning Control

School of Computer and Software Engineering, Shenzhen Polytechnic, Shenzhen 518055, China

Received 18 November 2013; Accepted 27 January 2014; Published 5 March 2014

Academic Editor: Jagannathan Sarangapani

Copyright © 2014 Xuefei Wu and Zhe Nie. 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. M. E. J. Newman, “The structure and function of complex networks,” SIAM Review, vol. 45, no. 2, pp. 167–256, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. G. Shinar and M. Feinberg, “Structural sources of robustness in biochemical reaction networks,” Science, vol. 327, no. 5971, pp. 1389–1391, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. A.-L. Barabási, “Scale-free networks: a decade and beyond,” Science, vol. 325, no. 5939, pp. 412–413, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. C. T. Butts, “Revisiting the foundations of network analysis,” Science, vol. 325, no. 5939, pp. 414–416, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Centola, “The spread of behavior in an online social network experiment,” Science, vol. 329, no. 5996, pp. 1194–1197, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. J.-W. Wang, Q. H. Ma, L. Zeng, and M. S. Abd-Elouahab, “Mixed outer synchronization of coupled complex networks with time-varying coupling delay,” Chaos, vol. 21, no. 1, Article ID 013121, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Q. T. Gan, R. Xu, and X. B. Kang, “Synchronization of chaotic neural networks with mixed time delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 966–974, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Q. X. Zhu and J. D. Cao, “Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 2139–2159, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Prasad, J. Kurths, and R. Ramaswamy, “The effect of time-delay on anomalous phase synchronization,” Physics Letters A, vol. 372, no. 40, pp. 6150–6154, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. D. V. Senthilkumar, M. Lakshmanan, and J. Kurths, “Transition from phase to generalized synchronization in time-delay systems,” Chaos, vol. 18, no. 2, Article ID 023118, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhysics letters, vol. 93, no. 6, Article ID 60003, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. C.-K. Zhang, Y. He, and M. Wu, “Exponential synchronization of neural networks with time-varying mixed delays and sampled-data,” Neurocomputing, vol. 74, no. 1–3, pp. 265–273, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. K. S. Sudheer and M. Sabir, “Adaptive modified function projective synchronization of multiple time-delayed chaotic Rössler system,” Physics Letters A, vol. 375, no. 8, pp. 1176–1178, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. C. K. Ahn, “Anti-synchronization of time-delayed chaotic neural networks based on adaptive control,” International Journal of Theoretical Physics, vol. 48, no. 12, pp. 3498–3509, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. Z.-M. Ge, Y.-T. Wong, and S.-Y. Li, “Temporary lag and anticipated synchronization and anti-synchronization of uncoupled time-delayed chaotic systems,” Journal of Sound and Vibration, vol. 318, no. 1-2, pp. 267–278, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. C. K. Ahn, “Adaptive H anti-synchronization for time-delayed chaotic neural networks,” Progress of Theoretical Physics, vol. 122, no. 6, pp. 1391–1403, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Zhang and J. A. Xu, “Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 164–174, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Z. Y. Wu, J. Duan, and X. C. Fu, “Complex projective synchronization in coupled chaotic complex dynamical systems,” Nonlinear Dynamics, vol. 69, no. 3, pp. 771–779, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. H. Y. Du, P. Shi, and N. Lü, “Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control,” Nonlinear Analysis: Real World Applications, vol. 14, no. 2, pp. 1182–1190, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J.-G. Liu, “Generalized projective synchronization of fractional-order complex networks with nonidentical nodes,” Chinese Physics B, vol. 21, no. 12, Article ID 120506, 2012. View at Publisher · View at Google Scholar
  21. H.-X. Yao and S.-G. Wang, “Cluster projective synchronization of complex networks with nonidentical dynamical nodes,” Chinese Physics B, vol. 21, no. 11, Article ID 110506, 2012. View at Publisher · View at Google Scholar
  22. Z. Y. Wu and X. C. Fu, “Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems,” Nonlinear Dynamics, vol. 72, no. 1-2, pp. 9–15, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Q. T. Gan, R. Xu, and X. B. Kang, “Synchronization of chaotic neural networks with mixed time delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 966–974, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. X. J. Wu and H. T. Lu, “Generalized projective synchronization between two different general complex dynamical networks with delayed coupling,” Physics Letters A, vol. 374, no. 38, pp. 3932–3941, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. D. Ghosh, “Generalized projective synchronization in time-delayed systems: nonlinear observer approach,” Chaos, vol. 19, no. 1, Article ID 013102, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  26. D. Ghosh, S. Banerjee, and A. R. Chowdhury, “Generalized and projective synchronization in modulated time-delayed systems,” Physics Letters A, vol. 374, no. 21, pp. 2143–2149, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. D. Ghosh, P. Saha, and A. R. Chowdhury, “Linear observer based projective synchronization in delay Rössler system,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 6, pp. 1640–1647, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. J. R. Chen, L. C. Jiao, J. S. Wu, and X. D. Wang, “Projective synchronization with different scale factors in a drivenresponse complex network and its application in image encryption,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 3045–3058, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. W. Wu, W. Zhou, and T. P. Chen, “Cluster synchronization of linearly coupled complex networks under pinning control,” IEEE Transactions on Circuits and Systems, vol. 56, no. 4, pp. 829–839, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  30. C. Yuan and X. Mao, “Robust stability and controllability of stochastic differential delay equations with Markovian switching,” Automatica, vol. 40, no. 3, pp. 343–354, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. S. Cai, J. Zhou, L. Xiang, and Z. 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 · View at Scopus
  32. Y. Yang and J. Cao, “Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1650–1659, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. W. Zhu, D. Xu, and Y. Huang, “Global impulsive exponential synchronization of time-delayed coupled chaotic systems,” Chaos, Solitons & Fractals, vol. 35, no. 5, pp. 904–912, 2008. View at Publisher · View at Google Scholar · View at Scopus
  34. C. Xu, J. Wang, and J. Feng, “Impulsive pinning Markovian switching stochastic complex networks with time-varying delay,” Mathematical Problems in Engineering, vol. 2013, Article ID 461924, 9 pages, 2013. View at Publisher · View at Google Scholar
  35. X. W. Liu and T. P. Chen, “Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling,” Physica A, vol. 381, no. 1-2, pp. 82–92, 2007. View at Publisher · View at Google Scholar · View at Scopus
  36. C. Perret, The stability of numerical simulations of complex stochastic differential equations [Ph.D. thesis], ETH Zurich, Zurich, Switzerland, 2010.