About this Journal Submit a Manuscript Table of Contents
Journal of Applied Mathematics
Volume 2014 (2014), Article ID 972608, 6 pages
http://dx.doi.org/10.1155/2014/972608
Research Article

Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

1School of Mathematical Science, Ocean University of China, Qingdao 266100, China
2School of Mathematical Science, Liaocheng University, Liaocheng 252059, China

Received 24 July 2013; Accepted 12 December 2013; Published 12 January 2014

Academic Editor: Subhas Abel

Copyright © 2014 Guiying Chen and Linshan Wang. 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. Z. Wu, J. Lam, H. Su, et al., “Stability and dissipativity analysis of static neural networks with time delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 2, pp. 199–210, 2012.
  2. L. Wang, R. Zhang, and Y. Wang, “Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 1101–1113, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. Q. Duan, H. Su, and Z. Wu, “H state estimation of static neural networks with time-varying delay,” Neurocomputing, vol. 97, no. 15, pp. 16–21, 2012.
  4. L. Wan and D. Xu, “Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays,” Science in China F, vol. 46, no. 6, pp. 466–474, 2003.
  5. D. Xu and S. Long, “Attracting and quasi-invariant sets of non-autonomous neural networks with delays,” Neurocomputing, vol. 77, no. 1, pp. 222–228, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. L. Wang and D. Xu, “Global asymptotic stability of bidirectional associative memory neural networks with S-type distributed delays,” International Journal of Systems Science, vol. 33, no. 11, pp. 869–877, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. L. Wang, Recurrent Neural Networks with Time Delays, Science Press, Beijing, China, 2008.
  8. C. Huang and J. Cao, “Almost sure exponential stability of stochastic cellular neural networks with unbounded distributed delays,” Neurocomputing, vol. 72, no. 13-15, pp. 3352–3356, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. Z.-G. Wu, J. H. Park, H. Su, and J. Chu, “New results on exponential passivity of neural networks with time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 13, no. 4, pp. 1593–1599, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. W. Han, Y. Kao, and L. Wang, “Global exponential robust stability of static interval neural networks with S-type distributed delays,” Journal of the Franklin Institute, vol. 348, no. 8, pp. 2072–2081, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, vol. 74, Kluwer Academic, Dordrecht, The Netherlands, 1992. View at MathSciNet
  12. 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 Scopus
  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 Scopus
  14. C. Li and T. Huang, “On the stability of nonlinear systems with leakage delay,” Journal of the Franklin Institute, vol. 346, no. 4, pp. 366–377, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. X. Li, X. Fu, P. Balasubramaniam, and R. Rakkiyappan, “Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4092–4108, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. M. J. Park, O. M. Kwon, J. H. Park, S. M. Lee, and E. J. Cha, “Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay,” Journal of the Franklin Institute, vol. 349, no. 5, pp. 1699–1720, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Peng, “Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 2141–2151, 2010. View at Publisher · View at Google Scholar · View at Scopus
  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 Scopus
  19. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1979. View at MathSciNet
  20. D. Xu and Z. Yang, “Attracting and invariant sets for a class of impulsive functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 329, no. 2, pp. 1036–1044, 2007. View at Publisher · View at Google Scholar · View at Scopus