Table of Contents
Advances in Artificial Neural Systems
Volume 2013 (2013), Article ID 908602, 5 pages
http://dx.doi.org/10.1155/2013/908602
Research Article

Globally Exponential Stability of Impulsive Neural Networks with Given Convergence Rate

Department of Mathematics, Shandong Normal University, Ji'nan 250014, China

Received 29 November 2012; Accepted 12 April 2013

Academic Editor: Manwai Mak

Copyright © 2013 Chengyan Liu 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. Z. Yang and D. Xu, “Stability analysis of delay neural networks with impulsive effects,” IEEE Transactions on Circuits and Systems II, vol. 52, no. 1, pp. 517–521, 2005. View at Publisher · View at Google Scholar
  2. J. Cao, “Global stability analysis in delayed cellular neural networks,” Physical Review E, vol. 59, no. 5, pp. 5940–5944, 1999. View at Publisher · View at Google Scholar
  3. J. Shen, Y. Liu, and J. Li, “Asymptotic behavior of solutions of nonlinear neutral differential equations with impulses,” Journal of Mathematical Analysis and Applications, vol. 332, no. 1, pp. 179–189, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. B. Kosko, Neural Networks and Fuzzy Systems, Prentice Hall, New Delhi, India, 1992.
  5. J. Cao, “On stability of delayed cellular neural networks,” Physics Letters A, vol. 261, no. 5-6, pp. 303–308, 1999. View at Publisher · View at Google Scholar
  6. K. Gopalsamy, “Stability of artificial neural networks with impulses,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 783–813, 2004. View at Publisher · View at Google Scholar · View at Scopus
  7. R. Samidurai, S. Marshal Anthoni, and K. Balachandran, “Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 1, pp. 103–112, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. B. Lisena, “Exponential stability of Hopfield neural networks with impulses,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 1923–1930, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Wu, C. Li, X. Liao, and S. Duan, “Exponential stability of impulsive discrete systems with time delay and applications in stochastic neural networks: a Razumikhin approach,” Neurocomputing, vol. 82, pp. 29–36, 2012. View at Publisher · View at Google Scholar
  10. A. Berman and R. J. Plemmons, Nonnegative Matrices in The Mathematical Sciences, Academic Press, New York, NY, USA, 1979. View at MathSciNet
  11. D. D. Baĭnov and P. S. Simeonov, Systems with Impulsive Effect Stability Theory and Applications, Halsted Press, New York, NY, USA, 1989. View at MathSciNet
  12. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. View at MathSciNet
  13. X. L. Fu, B. Q. Yan, and Y. S. Liu, Introduction of Impulsive Differential Systems, Science Press, Beijing, China, 2005.
  14. I. M. Stamova, Stability Analysis of Impulsive Functional Differential Equations, Walter de Gruyter, New York, NY, USA, 2009.
  15. X. Liu and Q. Wang, “The method of Lyapunov functionals and exponential stability of impulsive systems with time delay,” Nonlinear Analysis: Theory, Methods and Applications, vol. 66, no. 7, pp. 1465–1484, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. X. D. Li, “New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4194–4201, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. X. Z. Liu, “Stability of impulsive control systems with time delay,” Mathematical and Computer Modelling, vol. 39, no. 4-5, pp. 511–519, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  18. X. Fu and X. Li, “Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays,” Journal of Computational and Applied Mathematics, vol. 231, no. 1, pp. 187–199, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. 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
  20. X. D. Li and Z. Chen, “Stability properties for Hopfield neural networks with delays and impulsive perturbations,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 3253–3265, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. X. D. Li and M. Bohner, “Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback,” Mathematical and Computer Modelling, vol. 52, no. 5-6, pp. 643–653, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. H. Akça, R. Alassar, V. Covachev, Z. Covacheva, and E. Al-Zahrani, “Continuous-time additive Hopfield-type neural networks with impulses,” Journal of Mathematical Analysis and Applications, vol. 290, no. 2, pp. 436–451, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. Z. T. Huang, Q. G. Yang, and X. S. Luo, “Exponential stability of impulsive neural networks with time-varying delays,” Chaos, Solitons and Fractals, vol. 35, no. 4, pp. 770–780, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. I. M. Stamova and R. Ilarionov, “On global exponential stability for impulsive cellular neural networks with time-varying delays,” Computers and Mathematics with Applications, vol. 59, no. 11, pp. 3508–3515, 2010. View at Publisher · View at Google Scholar · View at Scopus