Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 138379, 11 pages
http://dx.doi.org/10.1155/2014/138379
Research Article

Global Exponential Stability of Antiperiodic Solution for Impulsive High-Order Hopfield Neural Networks

1School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China
2College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China

Received 27 August 2013; Accepted 11 January 2014; Published 19 March 2014

Academic Editor: Douglas Anderson

Copyright © 2014 Wei Chen and Shuhua Gong. 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. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. View at MathSciNet
  2. A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14, World Scientific, Singapore, 1995. View at MathSciNet
  3. M. U. Akhmet, “On the general problem of stability for impulsive differential equations,” Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 182–196, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. P. Shi and L. Dong, “Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses,” Applied Mathematics and Computation, vol. 216, no. 2, pp. 623–630, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. B. Xu, X. Liu, and X. Liao, “Global asymptotic stability of high-order Hopfield type neural networks with time delays,” Computers & Mathematics with Applications, vol. 45, no. 10-11, pp. 1729–1737, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. Zhang, “Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays,” Advances in Difference Equations, vol. 2013, article 162, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  7. B. Liu and S. Gong, “Periodic solution for impulsive cellar neural networks with time-varying delays in the leakage terms,” Abstract and Applied Analysis, vol. 2013, Article ID 701087, 10 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y. Li, L. Zhao, and P. Liu, “Existence and exponential stability of periodic solution of high-order Hopfield neural network with delays on time scales,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 573534, 18 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. B. Xiao and H. Meng, “Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks,” Applied Mathematical Modelling, vol. 33, no. 1, pp. 532–542, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. F. Zhang and Y. Li, “Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions,” Electronic Journal of Differential Equations, vol. 99, pp. 1–10, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. Ou, “Anti-periodic solutions for high-order Hopfield neural networks,” Computers & Mathematics with Applications, vol. 56, no. 7, pp. 1838–1844, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. W. Yang, “Existence and stability of periodic solutions of BAM high-order Hopfield neural networks with impulses and delays on time scales,” Electronic Journal of Differential Equations, vol. 8, pp. 1–22, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Wang and L. Wang, “LMI-based approach for exponential robust stability of high-order Hopfield neural networks with time-varying delays,” Journal of Applied Mathematics, vol. 2012, Article ID 182745, 8 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. L. Zhao and Y. Li, “Existence and exponential stability of anti-periodic solutions of high-order Hopfield neural networks with delays on time scales,” Differential Equations and Dynamical Systems, vol. 19, no. 1-2, pp. 13–26, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. 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
  16. 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
  17. S. Peng, “Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms,” Nonlinear Analysis, vol. 11, no. 3, pp. 2141–2151, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. B. Liu, “Global exponential stability for BAM neural networks with time-varying delays in the leakage terms,” Nonlinear Analysis, vol. 14, no. 1, pp. 559–566, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. H. Zhang and J. Shao, “Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms,” Applied Mathematics and Computation, vol. 219, no. 24, pp. 11471–11482, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  20. W. Wang, “Anti-periodic solution for impulsive high-order Hopfield neural networks with time-varying delays in the leakage terms,” Advances in Difference Equations, vol. 2013, article 273, 2013. View at Publisher · View at Google Scholar · View at MathSciNet