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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 543549, 14 pages
http://dx.doi.org/10.1155/2013/543549
Research Article

Synchronization of Chaotic Delayed Fuzzy Neural Networks under Impulsive and Stochastic Perturbations

1College of Science, Chongqing Jiaotong University, Chongqing 400074, China
2Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China

Received 4 October 2012; Revised 3 December 2012; Accepted 14 December 2012

Academic Editor: Xiaodi Li

Copyright © 2013 Bing Li and Qiankun Song. 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. T. Yang and L. Yang, “The global stability of fuzzy cellular neural network,” IEEE Transactions on Circuits and Systems I, vol. 43, no. 10, pp. 880–883, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  2. T. Yang and L. Yang, “Fuzzy cellular neural network: a new paradigm for image processing,” International Journal of Circuit Theory and Applications, vol. 25, no. 6, pp. 469–481, 1997. View at Scopus
  3. Y. Liu and W. Tang, “Exponential stability of fuzzy cellular neural networks with constant and time-varying delays,” Physics Letters A, vol. 323, no. 3-4, pp. 224–233, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. T. Huang, “Exponential stability of delayed fuzzy cellular neural networks with diffusion,” Chaos, Solitons & Fractals, vol. 31, no. 3, pp. 658–664, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Niu, H. Jiang, and Z. Teng, “Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays,” Neurocomputing, vol. 71, no. 13–15, pp. 2929–2936, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. L. Chen and H. Zhao, “Stability analysis of stochastic fuzzy cellular neural networks with delays,” Neurocomputing, vol. 72, no. 1–3, pp. 436–444, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. H. Zhao, N. Ding, and L. Chen, “Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays,” Chaos, Solitons & Fractals, vol. 40, no. 4, pp. 1653–1659, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. X. Wang and D. Xu, “Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms,” Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 2713–2721, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. X. Li, R. Rakkiyappan, and P. Balasubramaniam, “Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 135–155, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. Balasubramaniam, M. Kalpana, and R. Rakkiyappan, “Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 839–853, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. M. Syed and P. Balasubramaniam, “Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2907–2916, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. Balasubramaniam, M. Kalpana, and R. Rakkiyappan, “State estimation for fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays,” Computers & Mathematics with Applications, vol. 62, no. 10, pp. 3959–3972, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. F. Zou and J. Nossek, “Bifurcation and chaos in cellular neural networks,” IEEE Transactions on Circuits and Systems I, vol. 40, no. 3, pp. 166–173, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. Lu, “Chaotic attractors in delayed neural networks,” Physics Letters A, vol. 298, no. 2-3, pp. 109–116, 2002. View at Publisher · View at Google Scholar · View at Scopus
  15. 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
  16. T. L. Liao and S. H. Tsai, “Adaptive synchronization of chaotic systems and its application to secure communications,” Chaos, Solitons & Fractals, vol. 11, no. 9, pp. 1387–1396, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Barahona and L. M. Pecora, “Synchronization in small-world systems,” Physical Review Letters, vol. 89, no. 5, article 054101, 2002. View at Scopus
  18. 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
  19. W. Yu and J. Cao, “Synchronization control of stochastic delayed neural networks,” Physica A, vol. 373, pp. 252–260, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. 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
  21. Q. Song, “Synchronization analysis of coupled connected neural networks with mixed time delays,” Neurocomputing, vol. 72, no. 16–18, pp. 3907–3914, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. T. Li, A. Song, S. Fei, and Y. Guo, “Synchronization control of chaotic neural networks with time-varying and distributed delays,” Nonlinear Analysis, vol. 71, no. 5-6, pp. 2372–2384, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. 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 Zentralblatt MATH · View at MathSciNet
  24. X. Yang, C. Huang, and Q. Zhu, “Synchronization of switched neural networks with mixed delays via impulsive control,” Chaos, Solitons & Fractals, vol. 44, no. 10, pp. 817–826, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  25. W. Ding and M. Han, “Synchronization of delayed fuzzy cellular neural networks based on adaptive control,” Physics Letters A, vol. 372, no. 26, pp. 4674–4681, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. Y. Xia, Z. Yang, and M. Han, “Synchronization schemes for coupled identical Yang-Yang type fuzzy cellular neural networks,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 9-10, pp. 3645–3659, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. L. Wang, W. Ding, and D. Chen, “Synchronization schemes of a class of fuzzy cellular neural networks based on adaptive control,” Physics Letters A, vol. 374, no. 13-14, pp. 1440–1449, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. J. Yu, C. Hu, H. Jiang, and Z. Teng, “Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control,” Mathematics and Computers in Simulation, vol. 82, no. 5, pp. 895–908, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. Z. Xing and J. Peng, “Exponential lag synchronization of fuzzy cellular neural networks with time-varying delays,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 1074–1086, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  30. W. Ding, “Synchronization of delayed fuzzy cellular neural networks with impulsive effects,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 11, pp. 3945–3952, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. X. Feng, F. Zhang, and W. Wang, “Global exponential synchronization of delayed fuzzy cellular neural networks with impulsive effects,” Chaos, Solitons & Fractals, vol. 44, no. 1–3, pp. 9–16, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. Q. Gan, R. Xu, and P. Yang, “Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1862–1870, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. A. Friedman, Stochastic Differential Equations and Applications, Academic Press, NewYork, NY, USA, 1975.
  34. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985. View at MathSciNet
  35. Z. Yang and D. Xu, “Robust stability of uncertain impulsive control systems with time-varying delay,” Computers & Mathematics with Applications, vol. 53, no. 5, pp. 760–769, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. Z. Yang, D. Xu, and L. Xiang, “Exponential p-stability of impulsive stochastic differential equations with delays,” Physics Letters A, vol. 359, no. 2, pp. 129–137, 2006. View at Publisher · View at Google Scholar · View at MathSciNet