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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 307981, 14 pages
http://dx.doi.org/10.1155/2013/307981
Research Article

Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

1College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, Hunan 415000, China
2Nanhu College, Jiaxing University, Jiaxing, Zhejiang 314001, China

Received 13 November 2012; Revised 23 January 2013; Accepted 24 January 2013

Academic Editor: Wenchang Sun

Copyright © 2013 Hong Zhang and Mingquan Yang. 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. H. Park, “Further result on asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1661–1666, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. X. Li, C. Ding, and Q. Zhu, “Synchronization of stochastic perturbed chaotic neural networks with mixed delays,” Journal of the Franklin Institute, vol. 347, no. 7, pp. 1266–1280, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. O. M. Kwon and J. H. Park, “Delay-dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays,” Journal of the Franklin Institute, vol. 345, no. 7, pp. 766–778, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Wang, “Stability of Cohen-Grossberg neural networks with distributed delays,” Applied Mathematics and Computation, vol. 160, no. 1, pp. 93–110, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Bouzerdoum and R. B. Pinter, “Shunting inhibitory cellular neural networks: derivation and stability analysis,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 40, no. 3, pp. 215–221, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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.
  7. 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
  8. 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, pp. 177–186, 2006. View at Google Scholar
  9. Q. Fan and J. Shao, “Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying and continuously distributed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 6, pp. 1655–1663, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Q. Zhou and C. Zhao, “Exponential convergence of shunting inhibitory cellular neural networks with continuously distributed delays,” Annales Polonici Mathematici, vol. 98, no. 3, pp. 241–250, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. 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
  12. Z. Chen, “A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type,” Neural Computing and Applications, 2012. View at Publisher · View at Google Scholar
  13. K. Gopalsamy, “Leakage delays in BAM,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1117–1132, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. B. Kosko, Neural Networks and Fuzzy Systems, Prentice-Hall, Englewood Cliffs, NJ, USA, 1992. View at MathSciNet
  15. S. Haykin, Neural Networks, Prentice Hall, New Jersey, NY, USA, 1999.
  16. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, vol. 74 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992. View at MathSciNet
  17. X. Li and J. Cao, “Delay-dependent stability of neural networks of neutral type with time delay in the leakage term,” Nonlinearity, vol. 23, no. 7, pp. 1709–1726, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. X. Li, R. Rakkiyappan, and P. Balasubramaniam, “Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 135–155, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. P. Balasubramaniam, V. Vembarasan, and R. Rakkiyappan, “Leakage delays in T-S fuzzy cellular neural networks,” Neural Processing Letters, vol. 33, pp. 111–136, 2011. View at Google Scholar
  20. B. Liu, “Global exponential stability for BAM neural networks with time-varying delays in the leakage terms,” Nonlinear Analysis. Real World Applications, vol. 14, no. 1, pp. 559–566, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  21. Z. Chen and M. Yang, “Exponential convergence for HRNNs with continuously distributed delays in the leakage terms,” Neural Computing & Applications, 2012. View at Publisher · View at Google Scholar
  22. A. M. Fink, Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974. View at MathSciNet
  23. C. Y. He, Almost Periodic Differential Equation, House, Higher Education Publishing, Beijing, China, 1992.