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Abstract and Applied Analysis
Volume 2010, Article ID 915451, 20 pages
http://dx.doi.org/10.1155/2010/915451
Research Article

Existence and Global Exponential Stability of Almost Periodic Solutions for SICNNs with Nonlinear Behaved Functions and Mixed Delays

1Department of Mathematics, Honghe University, Mengzi Yunnan 661100, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3Department of Mathematics, College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, China

Received 9 July 2009; Accepted 2 February 2010

Academic Editor: Allan C. Peterson

Copyright © 2010 Xinsong Yang 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. A. Bouzerdoum and R. B. Pinter, “Shunting inhibitory cellular neural networks: derivation and stability analysis,” IEEE Transactions on Circuits and Systems I, vol. 40, no. 3, pp. 215–221, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Bouzerdoum and R. B. Pinter, “Analysis and analog implementation of directionally sensitive shunting inhibitory cellular neural networks,” in Visual Information Processing: From Neurons to Chips, vol. 1473 of Proceedings of SPIE, pp. 29–38, 1991. View at Scopus
  3. A. Bouzerdoum and R. B. Pinter, “Nonlinear lateral inhibition applied to motion detection in the fly visual system,” in Nonlinear Vision, R. B. Pinter and B. Nabet, Eds., pp. 423–450, CRC Press, Boca Raton, Fla, USA, 1992. View at Google Scholar
  4. K. Gopalsamy and X. Z. He, “Stability in asymmetric hopfield nets with transmission delays,” Physica D, vol. 76, no. 4, pp. 344–358, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Y. Li, C. Liu, and L. Zhu, “Global exponential stability of periodic solution of shunting inhibitory CNNs with delays,” Physics Letters A, vol. 337, pp. 46–54, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. H. Meng and Y. Li, “New convergence behavior of shunting inhibitory cellular neural networks with time-varying coefficients,” Applied Mathematics Letters, vol. 21, no. 7, pp. 717–721, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. B. Liu and L. Huang, “Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays,” Physics Letters A, vol. 349, no. 1–4, pp. 177–186, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. B. Liu and L. Huang, “Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 211–217, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Q. Zhou, B. Xiao, Y. Yu, and L. Peng, “Existence and exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays,” Chaos, Solitons and Fractals, vol. 34, no. 3, pp. 860–866, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. Chen and J. Cao, “Almost periodic solution of shunting inhibitory CNNs with delays,” Physics Letters A, vol. 298, no. 2-3, pp. 161–170, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. X. Huang and J. Cao, “Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay,” Physics Letters A, vol. 314, no. 3, pp. 222–231, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Chen and H. Zhao, “Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients,” Chaos, Solitons and Fractals, vol. 35, no. 2, pp. 351–357, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Xia, J. Cao, and Z. Huang, “Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses,” Chaos, Solitons and Fractals, vol. 34, no. 5, pp. 1599–1607, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C. Ou, “Almost periodic solutions for shunting inhibitory cellular neural networks,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 2652–2658, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. W. Zhao and H. Zhang, “On almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients and time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 9, no. 5, pp. 2326–2336, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. Shao, L. Wang, and C. Ou, “Almost periodic solutions for shunting inhibitory cellular neural networks without global Lipschitz activity functions,” Applied Mathematical Modelling, vol. 33, no. 6, pp. 2575–2581, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  17. H. Ding, J. Liang, and T. Xiao, “Existence of almost periodic solutions for SICNNs with time-varying delays,” Physics Letters A, vol. 372, no. 33, pp. 5411–5416, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  18. B. Liu, “New convergence behavior of solutions to shunting inhibitory cellular neural networks with unbounded delays and time-varying coefficients,” Applied Mathematical Modelling, vol. 33, no. 1, pp. 54–60, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Y. Li and L. Huang, “Exponential convergence behavior of solutions to shunting inhibitory cellular neural networks with delays and time-varying coefficients,” Mathematical and Computer Modelling, vol. 48, no. 3-4, pp. 499–504, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Y. Li, H. Meng, and Q. Zhou, “Exponential convergence behavior of shunting inhibitory cellular neural networks with time-varying coefficients,” Journal of Computational and Applied Mathematics, vol. 216, no. 1, pp. 164–169, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. Shao, L. Wang, and C. Ou, “Almost periodic solutions for shunting inhibitory cellular neural networks without global Lipschitz activity functions,” Applied Mathematical Modelling, vol. 33, no. 6, pp. 2575–2581, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  22. C. Y. He, Almost Periodic Differential Equation, Higher Education, Beijing, China, 1992.
  23. E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, Germany, 1965. View at MathSciNet