About this Journal Submit a Manuscript Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 405939, 10 pages
http://dx.doi.org/10.1155/2012/405939
Research Article

Stability of the Stochastic Reaction-Diffusion Neural Network with Time-Varying Delays and p-Laplacian

1College of Civil Engineering and Architecture, Sanming University, Sanming 365004, China
2Department of Mathematics and Physics, Huaihai Institute of Technology, Lianyungang 222005, China
3Science and Technology on Microsystems Laboratory, Shanghai Institute of MicroSystems and Information Technology, CAS, Shanghai 200050, China

Received 22 October 2012; Accepted 9 November 2012

Academic Editor: Maoan Han

Copyright © 2012 Pan Qingfei 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. X. Liao and J. Wang, “Global dissipativity of continuous-time recurrent neural networks with time delay,” Physical Review E, vol. 68, no. 1, Article ID 016118, 6 pages, 2003. View at Publisher · View at Google Scholar
  2. L. Wang and D. Xu, “Stability for Hopfield neural networks with time delay,” Journal of Vibration and Control, vol. 8, no. 1, pp. 13–18, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. D. Xu, H. Zhao, and H. Zhu, “Global dynamics of Hopfield neural networks involving variable delays,” Computers & Mathematics with Applications, vol. 42, no. 1-2, pp. 39–45, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. L. S. Wang and D. Y. Xu, “Stability analysis of Hopfield neural networks with time delay,” Applied Mathematics and Mechanics, vol. 23, no. 1, pp. 65–70, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. X. Liao, X. Mao, J. Wang, and Z. Zeng, “Algebraic conditions of stability for Hopfield neural network,” Science in China F, vol. 47, no. 1, pp. 113–125, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. X. X. Liao, S. Z. Yang, S. J. Cheng, and Y. Shen, “Stability of general neural networks with reaction-diffusion,” Sciena in China E, vol. 32, no. 1, pp. 87–94, 2002 (Chinese).
  7. L. Wang and D. Xu, “Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays,” Science in China F, vol. 46, no. 6, pp. 466–474, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. S. Blythe, X. Mao, and X. Liao, “Stability of stochastic delay neural networks,” Journal of the Franklin Institute, vol. 338, no. 4, pp. 481–495, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. Hu, X. Liao, and X. Mao, “Stochastic Hopfield neural networks,” Journal of Physics A, vol. 36, pp. 2235–2249, 2003.
  10. J. R. Niu, Z. F. Zhang, and D. Y. Xu, “Exponential stability in mean square of a stochastic Cohen-Grossberg neural network with time-varying delays,” Chinese Journal of Engineering Mathematics, vol. 22, no. 6, pp. 1001–1005, 2005 (Chinese).
  11. Y. Shen, M. H. Jiang, and H. S. Yao, “Exponential stability of cellular neural networks,” Acta Mathematica Scientia A, vol. 25, no. 2, pp. 264–268, 2005 (Chinese).
  12. Q. Luo, F. Deng, J. Bao, B. Zhao, and Y. Fu, “Stabilization of stochastic Hopfield neural network with distributed parameters,” Science in China F, vol. 47, no. 6, pp. 752–762, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. Z. Zifang, The stability of uncertain dynamical systems and applications [M.S. thesis], Sichuan University, 2004.
  14. S. J. Long and L. Xiang, “A nonlinear measure method for stability of Hopfield neural networks with time-varying delays,” Journal of Sichuan University, vol. 44, no. 2, pp. 249–252, 2007 (Chinese).
  15. Z.-F. Zhang and D.-Y. Xu, “A note on stability of stochastic delay neural networks,” Chinese Journal of Engineering Mathematics, vol. 27, no. 4, pp. 720–730, 2010. View at Zentralblatt MATH
  16. Z. F. Zhang and J. Deng, “Stability of stochastic reaction-diffusion Hopfield neural network with time-varying delays,” Journal of Sichuan University, vol. 47, no. 3, pp. 251–256, 2010. View at Zentralblatt MATH
  17. D. Xu, “Stability criteria of large-scale systems of the neutral type,” in Proceedings of the12th IMACS World Congress on Scientific Computations, R. Vichnevetsky, P. Borne, and J. Vignes, Eds., vol. 1, p. 213, Gerfidn-cite Scientifique, Pairs, France, 1988.
  18. W. Rudin, Real and Complex Analysis, McGraw-Hill, 1974.