Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 963081, 12 pages
http://dx.doi.org/10.1155/2014/963081
Research Article

Robust Adaptive Exponential Synchronization of Stochastic Perturbed Chaotic Delayed Neural Networks with Parametric Uncertainties

1School of Automation and Electronic Information, Sichuan University of Science & Engineering, Sichuan 643000, China
2Institute of Nonlinear Science and Engineering Computing, Sichuan University of Science & Engineering, Sichuan 643000, China

Received 27 December 2013; Revised 23 May 2014; Accepted 23 May 2014; Published 23 June 2014

Academic Editor: Yang Tang

Copyright © 2014 Yang Fang 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. C.-J. Cheng and C.-B. Cheng, “An asymmetric image cryptosystem based on the adaptive synchronization of an uncertain unified chaotic system and a cellular neural network,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 10, pp. 2825–2837, 2013. View at Publisher · View at Google Scholar · View at Scopus
  2. V. Perez-Munuzuri, V. Perez-Villar, and L. O. Chua, “Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 40, no. 3, pp. 174–181, 1993. View at Publisher · View at Google Scholar · View at Scopus
  3. J. J. Fox, C. Jayaprakash, D. Wang, and S. R. Campbell, “Synchronization in relaxation oscillator networks with conduction delays,” Neural Computation, vol. 13, no. 5, pp. 1003–1021, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. V. Milanovic and M. E. Za-ghloul, “Synchronization of chaotic neural networks and applications to communications,” International Journal of Bifurcation and Chaos, vol. 6, no. 12, pp. 2571–2585, 1996. View at Google Scholar
  5. T. Yang and L. O. Chua, “Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 44, no. 10, pp. 976–988, 1997. View at Publisher · View at Google Scholar · View at Scopus
  6. C. Li, X. Liao, and K.-W. Wong, “Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication,” Physica D: Nonlinear Phenomena, vol. 194, no. 3-4, pp. 187–202, 2004. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Meng and X.-Y. Wang, “Robust anti-synchronization of a class of delayed chaotic neural networks,” Chaos, vol. 17, no. 2, Article ID 023113, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. X. Li and J. Cao, “Adaptive synchronization for delayed neural networks with stochastic perturbation,” Journal of the Franklin Institute, vol. 345, no. 7, pp. 779–791, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. Q. Zhu and J. 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 Scopus
  10. H. Zhang, Y. Xie, Z. Wang, and C. Zheng, “Adaptive synchronization between two different chaotic neural networks with time delay,” IEEE Transactions on Neural Networks, vol. 18, no. 6, pp. 1841–1845, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. S. C. Jeong, D. H. Ji, J. H. Park, and S. C. Won, “Adaptive synchronization for uncertain chaotic neural networks with mixed time delays using fuzzy disturbance observer,” Applied Mathematics and Computation, vol. 219, no. 11, pp. 5984–5995, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. Tang, R. Qiu, J. Fang, Q. Miao, and M. Xia, “Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays,” Physics Letters A: General, Atomic and Solid State Physics, vol. 372, no. 24, pp. 4425–4433, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. Q. Zhu and J. Cao, “Adaptive synchronization of chaotic Cohen-Crossberg neural networks with mixed time delays,” Nonlinear Dynamics, vol. 61, no. 3, pp. 517–534, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. D. Zhang and J. 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 Scopus
  15. V. I. Utkin, Sliding Modes in Control and Optimization, Springer, Berlin, Germany, 2001.
  16. J. F. Heagy, T. L. Carroll, and L. M. Pecora, “Experimental and numerical evidence for riddled basins in coupled chaotic systems,” Physical Review Letters, vol. 73, no. 26, pp. 3528–3531, 1994. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Sun, J. Cao, and Z. Wang, “Exponential synchronization of stochastic perturbed chaotic delayed neural networks,” Neurocomputing, vol. 70, no. 13–15, pp. 2477–2485, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. J. H. Park, “Synchronization of cellular neural networks of neutral type via dynamic feedback controller,” Chaos, Solitons and Fractals, vol. 42, no. 3, pp. 1299–1304, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. X. Li and X. Fu, “Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 885–894, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. F. Ren and J. Cao, “Anti-synchronization of stochastic perturbed delayed chaotic neural networks,” Neural Computing and Applications, vol. 18, no. 5, pp. 515–521, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. G. Zhang, Y. Shen, and L. Wang, “Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays,” Neural Networks, vol. 46, pp. 1–8, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. T. Ma and J. Fu, “On the exponential synchronization of stochastic impulsive chaotic delayed neural networks,” Neurocomputing, vol. 74, no. 5, pp. 857–862, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. H. Zhang, T. Ma, G.-B. Huang, and Z. Wang, “Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 40, no. 3, pp. 831–844, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. X. Li and R. Rakkiyappan, “Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 6, pp. 1515–1523, 2013. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Zhang, T. Ma, J. Fu, and S.-C. Tong, “Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks,” Chinese Physics B, vol. 18, no. 9, pp. 3742–3750, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. Q. Gan, “Synchronization of unknown chaotic neural networks with stochastic perturbation and time delay in the leakage term based on adaptive control and parameter identification,” Neural Computing and Applications, vol. 22, no. 6, pp. 1095–1104, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. Q. Gan and Y. Liang, “Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control,” Journal of the Franklin Institute, vol. 349, no. 6, pp. 1955–1971, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. Q. Gan, “Synchronisation of chaotic neural networks with unknown parameters and random time-varying delays based on adaptive sampled-data control and parameter identification,” IET Control Theory and Applications, vol. 6, no. 10, pp. 1508–1515, 2012. View at Publisher · View at Google Scholar · View at Scopus
  29. 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
  30. X. Li, C. Ding, and Q. Zhu, “Synchronization of stochastic perturbed chaotic neural networks with mixed delays,” Journal of the Franklin Institute, vol. 347, no. 7, pp. 1266–1280, 2010. View at Publisher · View at Google Scholar · View at Scopus
  31. X. Mao, “A note on the LaSalle-type theorems for stochastic differential delay equations,” Journal of Mathematical Analysis and Applications, vol. 268, no. 1, pp. 125–142, 2002. View at Publisher · View at Google Scholar · View at Scopus
  32. H. K. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 1996.
  33. X. Yang, Q. Zhu, and C. Huang, “Lag stochastic synchronization of chaotic mixed time-delayed neural networks with uncertain parameters or perturbations,” Neurocomputing, vol. 74, no. 10, pp. 1617–1625, 2011. View at Publisher · View at Google Scholar · View at Scopus
  34. Y. Sun and J. Cao, “Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation,” Physics Letters A: General, Atomic and Solid State Physics, vol. 364, no. 3-4, pp. 277–285, 2007. View at Publisher · View at Google Scholar · View at Scopus
  35. B. Ksendal, Stochastic Differential Equations an Introduction with Applications, Springer, New York, NY, USA, 2005.
  36. Y. Wang, L. Xie, and C. E. de Souza, “Robust control of a class of uncertain nonlinear systems,” Systems and Control Letters, vol. 19, no. 2, pp. 139–149, 1992. View at Google Scholar · View at Scopus
  37. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pa, USA, 1994.
  38. D. J. Higham, “An algorithmic introduction to numerical simulation of stochastic differential equations,” SIAM Review, vol. 43, no. 3, pp. 525–546, 2001. View at Google Scholar · View at Scopus
  39. M. Gilli, “Strange attractors in delayed cellular neural networks,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 40, no. 11, pp. 849–853, 1993. View at Publisher · View at Google Scholar · View at Scopus
  40. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, 2001.
  41. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, “Synchronization in complex networks,” Physics Reports, vol. 469, no. 3, pp. 93–153, 2008. View at Publisher · View at Google Scholar · View at Scopus
  42. W. Zhang, Y. Tang, Q. Miao, and W. Du, “Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 8, pp. 1316–1326, 2013. View at Publisher · View at Google Scholar · View at Scopus
  43. W. Zhang, Y. Tang, X. Wu, and J. Fang, “Synchronization of nonlinear dynamical networks with heterogeneous impulses,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 61, no. 4, pp. 1220–1228, 2014. View at Google Scholar
  44. Y. Tang, H. Gao, W. Zou, and J. Kurths, “Distributed synchronization in networks of agent systems with nonlinearities and random switchings,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 43, no. 1, pp. 358–370, 2013. View at Publisher · View at Google Scholar · View at Scopus