About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 825643, 17 pages
http://dx.doi.org/10.1155/2012/825643
Research Article

Dynamical Analysis for High-Order Delayed Hopfield Neural Networks with Impulses

College of Physics and Electronics, Shandong Normal University, Jinan 250014, China

Received 25 June 2012; Accepted 3 September 2012

Academic Editor: José J. Oliveira

Copyright © 2012 Dengwang Li. 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. J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons,” Proceedings of the National Academy of Sciences of the United States of America, vol. 81, no. 10, pp. 3088–3092, 1984. View at Scopus
  2. J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proceedings of the National Academy of Sciences of the United States of America, vol. 79, no. 8, pp. 2554–2558, 1982. View at Publisher · View at Google Scholar
  3. Y. Kamp and M. Hasler, Recursive Neural Networks for Associative Memory, John Wiley & Sons, New York, NY, USA, 1990.
  4. R. L. Wang, Z. Tang, and Q. P. Cao, “A learning method in Hopfield neural network for combinatorial optimization problem,” Neurocomputing, vol. 48, pp. 1021–1024, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Zhang and G. Wang, “New criteria of global exponential stability for a class of generalized neural networks with time-varying delays,” Neurocomputing, vol. 70, no. 13–15, pp. 2486–2494, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. Q. Zhang, X. Wei, and J. Xu, “Global asymptotic stability of Hopfield neural networks with transmission delays,” Physics Letters A, vol. 318, no. 4-5, pp. 399–405, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. H. Zhao, “Global asymptotic stability of Hopfield neural network involving distributed delays,” Neural Networks, vol. 17, no. 1, pp. 47–53, 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. Z. H. Guan and G. R. Chen, “On delayed impulsive Hopfield neural networks,” Neural Networks, vol. 12, no. 2, pp. 273–280, 1999. View at Publisher · View at Google Scholar
  9. H. Akça, R. Alassar, V. Covachev, Z. Covacheva, and E. Al-Zahrani, “Continuous-time additive Hopfield-type neural networks with impulses,” Journal of Mathematical Analysis and Applications, vol. 290, no. 2, pp. 436–451, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. 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
  11. F. Ren and J. Cao, “Periodic solutions for a class of higher-order Cohen-Grossberg type neural networks with delays,” Computers & Mathematics with Applications, vol. 54, no. 6, pp. 826–839, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. X. Liu, K. L. Teo, and B. Xu, “Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 16, no. 6, pp. 1329–1339, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. X.-Y. Lou and B.-T. Cui, “Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 144–158, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. F. Ren and J. Cao, “LMI-based criteria for stability of high-order neural networks with time-varying delay,” Nonlinear Analysis. Real World Applications, vol. 7, no. 5, pp. 967–979, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. B. Xu, X. Liu, and X. Liao, “Global asymptotic stability of high-order Hopfield type neural networks with time delays,” Computers & Mathematics with Applications, vol. 45, no. 10-11, pp. 1729–1737, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. Z. Guan, D. Sun, and J. Shen, “Qualitative analysis of high-order hopfield neural networks,” Acta Electronica Sinica, vol. 28, no. 3, pp. 77–80, 2000. View at Scopus
  17. J. Cao, “Global exponential stability of Hopfield neural networks,” International Journal of Systems Science. Principles and Applications of Systems and Integration, vol. 32, no. 2, pp. 233–236, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. S. Xu and J. Lam, “A new approach to exponential stability analysis of neural networks with time-varying delays,” Neural Networks, vol. 19, no. 1, pp. 76–83, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. F. Ren and J. Cao, “Periodic oscillation of higher-order bidirectional associative memory neural networks with periodic coefficients and delays,” Nonlinearity, vol. 20, no. 3, pp. 605–629, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. J. Cao, J. Liang, and J. Lam, “Exponential stability of high-order bidirectional associative memory neural networks with time delays,” Physica D, vol. 199, no. 3-4, pp. 425–436, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. R. Rakkiyappan and P. Balasubramaniam, “On exponential stability results for fuzzy impulsive neural networks,” Fuzzy Sets and Systems, vol. 161, no. 13, pp. 1823–1835, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. P. Balasubramaniam and V. Vembarasan, “Robust stability of uncertain fuzzy BAM neural networks of neutral-type with Markovian jumping parameters and impulses,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 1838–1861, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. P. Balasubramaniam and V. Vembarasan, “Asymptotic stability of BAM neural networks of neutral-type with impulsive effects and time delay in the leakage term,” International Journal of Computer Mathematics, vol. 88, no. 15, pp. 3271–3291, 2011. View at Publisher · View at Google Scholar
  24. D. D. Baĭnov and P. S. Simeonov, Systems with Impulse Effect Stability, Theory and Applications, Ellis Horwood, New York, NY, USA, 1989.
  25. X. L. Fu, B. Q. Yan, and Y. S. Liu, Introduction of Impulsive Differential Systems, Science Press, Beijing, China, 2005.
  26. C. Li, W. Hu, and S. Wu, “Stochastic stability of impulsive BAM neural networks with time delays,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 2313–2316, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. Y. Xia, Z. Huang, and M. Han, “Existence and globally exponential stability of equilibrium for BAM neural networks with impulses,” Chaos, Solitons & Fractals, vol. 37, no. 2, pp. 588–597, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific, Singapore, 1989.
  29. X. Li and J. Shen, “LMI approach for stationary oscillation of interval neural networks with discrete and distributed time-varying delays under impulsive perturbations,” IEEE Transactions on Neural Networks, vol. 21, no. 10, pp. 1555–1563, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. Y. Zhang and J. Sun, “Stability of impulsive neural networks with time delays,” Physics Letters, Section A, vol. 348, no. 1-2, pp. 44–50, 2005. View at Publisher · View at Google Scholar · View at Scopus
  31. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1979.