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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 415786, 14 pages
http://dx.doi.org/10.1155/2009/415786
Research Article

Periodic Solutions and Exponential Stability of a Class of Neural Networks with Time-Varying Delays

1Department of Mathematics, Qufu Normal University, Qufu 273165, Shandong, China
2Department of Mathematics, Shangqiu Normal University, Shangqiu 476000, Henan, China

Received 8 March 2009; Accepted 17 June 2009

Academic Editor: Guang Zhang

Copyright © 2009 Yingxin Guo and Mingzhi Xue. 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. S. Arik, “Global robust stability of delayed neural networks,” IEEE Transactions on Circuits and Systems I, vol. 50, no. 1, pp. 156–160, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. Dong, “Global exponential stability and existence of periodic solutions of CNNs with delays,” Physics Letters A, vol. 300, no. 1, pp. 49–57, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Chen, J. Cao, and L. Huang, “Global robust stability of interval cellular neural networks with time-varying delays,” Chaos, Solitons & Fractals, vol. 23, no. 3, pp. 787–799, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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
  5. T.-L. Liao and F.-C. Wang, “Global stability for cellular neural networks with time delay,” IEEE Transactions on Neural Networks, vol. 11, no. 6, pp. 1481–1484, 2000. View at Publisher · View at Google Scholar
  6. Y. Li, “Global exponential stability of BAM neural networks with delays and impulses,” Chaos, Solitons & Fractals, vol. 24, no. 1, pp. 279–285, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Cao, “On exponential stability and periodic solutions of CNNs with delays,” Physics Letters A, vol. 267, no. 5-6, pp. 312–318, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. 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, 7 pages, 2003. View at Google Scholar · View at MathSciNet
  9. H. Jiang and Z. Teng, “Global eponential stability of cellular neural networks with time-varying coefficients and delays,” Neural Networks, vol. 17, no. 10, pp. 1415–1425, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. Arik, “An analysis of global asymptotic stability of delayed cellular neural networks,” IEEE Transactions on Neural Networks, vol. 13, no. 5, pp. 1239–1242, 2002. View at Publisher · View at Google Scholar
  11. L. O. Chua and L. Yang, “Cellular neural networks: theory,” IEEE Transactions on Circuits and Systems, vol. 35, no. 10, pp. 1257–1272, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. T.-L. Liao and F.-C. Wang, “Global stability for cellular neural networks with time delay,” IEEE Transactions on Neural Networks, vol. 11, no. 6, pp. 1481–1484, 2000. View at Publisher · View at Google Scholar
  13. S Arik, “Stability analysis of delayed neural networks,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 7, pp. 1089–1092, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. L. Huang, C. Huang, and B. Liu, “Dynamics of a class of cellular neural networks with time-varying delays,” Physics Letters A, vol. 345, no. 4–6, pp. 330–344, 2005. View at Publisher · View at Google Scholar
  15. S. Mohamad and K. Gopalsamy, “Exponential stability of continuous-time and discrete-time cellular neural networks with delays,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 17–38, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. X. Lou and B. Cui, “Global asymptotic stability of delay BAM neural networks with impulses based on matrix theory,” Applied Mathematical Modelling, vol. 32, no. 2, pp. 232–239, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, Pa, USA, 1976. View at MathSciNet
  18. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985. View at MathSciNet
  19. R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, vol. 568 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977. View at MathSciNet
  20. J. Zhou, Z. Liu, and G. Chen, “Dynamics of periodic delayed neural networks,” Neural Networks, vol. 17, no. 1, pp. 87–101, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. Z. Liu and L. Liao, “Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays,” Journal of Mathematical Analysis and Applications, vol. 290, no. 1, pp. 247–262, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet