Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 576721, 13 pages
http://dx.doi.org/10.1155/2013/576721
Research Article

Global Exponential Stability Criteria for Bidirectional Associative Memory Neural Networks with Time-Varying Delays

1Department of Mathematics, Chiang Mai University, Chiang Mai 50200, Thailand
2Centre of Excellence in Mathematics CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 6 February 2013; Accepted 29 April 2013

Academic Editor: Yuming Chen

Copyright © 2013 J. Thipcha and P. Niamsup. 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. B. Kosko, “Adaptive bidirectional associative memories,” Applied Optics, vol. 26, no. 23, pp. 4947–4987, 1987. View at Google Scholar
  2. K. Ding, N. J. Huang, and X. Xu, “Global robust exponential stability of interval BAM neural network with mixed delays under uncertainty,” Neural Processing Letters, vol. 25, no. 2, pp. 127–141, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. C. Fu, W. Liu, and M. Yang, “Global exponential stability of a class of BAM neural networks with distributed delays,” in Proceedings of the 3rd International Workshop on Advanced Computational Intelligence (IWACI '10), pp. 11–15, August 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. M. Li, W. Chen, K. Li, X. Zhou, L. Zhao, and Y. Zhou, “Bi-directional reasoning based on BAM neural networks,” in Proceedings of the 2nd International Conference on Genetic and Evolutionary Computing (WGEC '08), pp. 141–144, September 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. X. Liao, J. Yu, and G. Chen, “Novel stability criteria for bidirectional associative memory neural networks with time delays,” International Journal of Circuit Theory and Applications, vol. 30, no. 5, pp. 519–546, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. J. Qiu and J. Cao, “An analysis for periodic solutions of high-order BAM neural networks with delays,” in Proceedings of the 2nd International Symposium on Neural Networks: Advances in Neural Networks (ISNN '05), Lecture Notes in Computer Science, pp. 288–293, Chongqing, China, June 2005. View at Scopus
  7. V. S. H. Rao and B. R. M. Phaneendra, “Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones,” Neural Networks, vol. 12, no. 3, pp. 455–465, 1999. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. P. Singh, V. S. Yadav, A. Gupta, and A. Khare, “Bidirection associative memory neural networks method in the character recognition,” Journal of Information Technology, Theory and Applications, pp. 382–386, 2009. View at Google Scholar
  9. Z. Zhang and K. Liu, “Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales,” Neural Networks, vol. 24, no. 5, pp. 427–439, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. D. Zhou and J. Cao, “Stability conditions for bi-directional associative memory neural networks with delay,” in Proceedings of the 3th World Congress on Intelligent Control and Automation, pp. 809–812, Beijing, China, July 2000. View at Scopus
  11. B. Kosko, “Bidirectional associative memories,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, no. 1, pp. 49–60, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Cao and M. Dong, “Exponential stability of delayed bi-directional associative memory networks,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 105–112, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. Cao and L. Wang, “Exponential stability and periodic oscillatory solution in BAM networks with delays,” IEEE Transactions on Neural Networks, vol. 13, no. 2, pp. 457–463, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. X. Huang, J. Cao, and D.-S. Huang, “LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks,” Chaos, Solitons & Fractals, vol. 24, no. 3, pp. 885–898, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C. Li, X. Liao, and R. Zhang, “Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach,” Chaos, Solitons & Fractals, vol. 24, no. 4, pp. 1119–1134, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. X. Liao and J. Yu, “Robust stability for interval Hopfield neural networks with time delay,” IEEE Transactions on Neural Networks, vol. 9, no. 5, pp. 1042–1045, 1998. View at Publisher · View at Google Scholar · View at Scopus
  17. X. Lou and B. Cui, “On the global robust asymptotic stability of BAM neural networks with time-varying delays,” Neurocomputing, vol. 70, no. 1–3, pp. 273–279, 2006. View at Publisher · View at Google Scholar · View at Scopus
  18. J. H. Park, “A novel criterion for global asymptotic stability of BAM neural networks with time delays,” Chaos, Solitons and Fractals, vol. 29, no. 2, pp. 446–453, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. A. Tian, M. Gai, B. Shi, and Q. Zhang, “Existence and exponential stability of periodic solution for a class of Cohen-Grossberg-type BAM neural networks,” Neurocomputing, vol. 73, no. 16–18, pp. 3147–3159, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Wang, Q. Song, and C. Duan, “LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions,” Mathematics and Computers in Simulation, vol. 81, no. 4, pp. 837–850, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. Y. Yuan and X. Li, “New results for global robust asymptotic stability of BAM neural networks with time-varying delays,” Neurocomputing, vol. 74, no. 1–3, pp. 337–342, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. E. Yucel and S. Arik, “New exponential stability results for delayed neural networks with time varying delays,” Physica D, vol. 191, no. 3-4, pp. 314–322, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Z. Zhang, Y. Yang, and Y. Huang, “Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays,” Neural Networks, vol. 24, no. 5, pp. 457–465, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. Y. Chen, S. Huang, J. Yin, and Q. Li, “Novel global exponential stability analysis for BAM neural networks with time-varying delays,” in Proceedings of Chinese Control and Decision Conference (CCDC '09), pp. 4355–4360, June 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. J. H. Park, S. M. Lee, and O. M. Kwon, “On exponential stability of bidirectional associative memory neural networks with time-varying delays,” Chaos, Solitons and Fractals, vol. 39, no. 3, pp. 1083–1091, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. L. Sheng and H. Yang, “Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2102–2113, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. G. Zong, Y. Wu, and L. Hou, “Global exponential stability for BAM neural networks with time-varying delays,” in Proceedings of the Chinese Control and Decision Conference (CCDC '08), pp. 2500–2505, Yantai, China, July 2008. View at Publisher · View at Google Scholar · View at Scopus
  28. P.-L. Liu, “Robust exponential stability for uncertain time-varying delay systems with delay dependence,” Journal of the Franklin Institute, vol. 346, no. 10, pp. 958–968, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. Y. Chen and T. Qin, “Improved global exponential stability criterion for BAM neural networks with time-varying delays,” Advances in Neural Network, pp. 128–137, 2008. View at Google Scholar