Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 506256, 17 pages
http://dx.doi.org/10.1155/2014/506256
Research Article

Global Exponential Stability of Weighted Pseudo-Almost Periodic Solutions of Neutral Type High-Order Hopfield Neural Networks with Distributed Delays

Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Received 13 May 2014; Accepted 27 August 2014; Published 3 December 2014

Academic Editor: Elena Braverman

Copyright © 2014 Lili Zhao and Yongkun Li. 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. Wang, J. Fang, and X. Liu, “Global stability of stochastic high-order neural networks with discrete and distributed delays,” Chaos, Solitons and Fractals, vol. 36, no. 2, pp. 388–396, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. Y. K. 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 Scopus
  3. S. Mohamad, “Exponential stability in Hopfield-type neural networks with impulses,” Chaos, Solitons and Fractals, vol. 32, no. 2, pp. 456–467, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. 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 MathSciNet · View at Scopus
  5. E. B. Kosmatopoulos and M. A. Christodoulou, “Structural properties of gradient recurrent high-order neural networks,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 42, no. 9, pp. 592–603, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. F. Zhang and Y. Li, “Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions,” Electronic Journal of Differential Equations, vol. 2007, no. 97, pp. 1–10, 2007. View at Google Scholar · View at MathSciNet
  7. X.-Y. Lou and B.-T. Cui, “Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 144–158, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. R. Rakkiyappan, C. Pradeep, A. Vinodkumar, and F. A. Rihan, “Dynamic analysis for high-order Hopfield neural networks with leakage delay and impulsive effects,” Neural Computing and Applications, vol. 22, no. 1, pp. 55–73, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. Q. Wang, Y. Fang, H. Li, L. Su, and B. Dai, “Anti-periodic solutions for high-order Hopfield neural networks with impulses,” Neurocomputing, vol. 138, pp. 339–346, 2014. View at Publisher · View at Google Scholar · View at Scopus
  10. J. H. Park, C. H. Park, O. M. Kwon, and S. M. Lee, “A new stability criterion for bidirectional associative memory neural networks of neutral-type,” Applied Mathematics and Computation, vol. 199, no. 2, pp. 716–722, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. R. Rakkiyappan and P. Balasubramaniam, “New global exponential stability results for neutral type neural networks with distributed time delays,” Neurocomputing, vol. 71, no. 4–6, pp. 1039–1045, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. R. Rakkiyappan and P. Balasubramaniam, “LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 317–324, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. C. Bai, “Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays,” Applied Mathematics and Computation, vol. 203, no. 1, pp. 72–79, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. B. Xiao, “Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays,” Applied Mathematics Letters, vol. 22, no. 4, pp. 528–533, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. H. Xiang and J. Cao, “Almost periodic solution of Cohen-Grossberg neural networks with bounded and unbounded delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 4, pp. 2407–2419, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. K. Wang and Y. Zhu, “Stability of almost periodic solution for a generalized neutral-type neural networks with delays,” Neurocomputing, vol. 73, no. 16–18, pp. 3300–3307, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. J. Liu and G. Zong, “New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type,” Neurocomputing, vol. 72, no. 10–12, pp. 2549–2555, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. R. Samli and S. Arik, “New results for global stability of a class of neutral-type neural systems with time delays,” Applied Mathematics and Computation, vol. 210, no. 2, pp. 564–570, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. R. Samidurai, S. M. 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 MathSciNet · View at Scopus
  20. R. Rakkiyappan, P. Balasubramaniam, and J. Cao, “Global exponential stability results for neutral-type impulsive neural networks,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 122–130, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Y. Li, L. Zhao, and X. Chen, “Existence of periodic solutions for neutral type cellular neural networks with delays,” Applied Mathematical Modelling, vol. 36, no. 3, pp. 1173–1183, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Y. Li and L. Yang, “Almost periodic solutions for neutral-type BAM neural networks with delays on time scales,” Journal of Applied Mathematics, vol. 2013, Article ID 942309, 13 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  23. Y. K. Li and Y. Q. Li, “Existence and exponential stability of almost periodic solution for neutral delay BAM neural networks with time-varying delays in leakage terms,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 350, no. 9, pp. 2808–2825, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. 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 MathSciNet · View at Scopus
  25. P. Balasubramaniam, G. Nagamani, and R. Rakkiyappan, “Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4422–4437, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. A. M. Fink, Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974. View at MathSciNet
  27. C. Y. He, Almost Periodic Differential Equations, Higher Education Publishing House, Beijing, China, 1992 (Chinese).
  28. T. Diagana, Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, Springer, Berlin , Germany, 2013. View at MathSciNet
  29. D. Ji and C. Zhang, “Translation invariance of weighted pseudo almost periodic functions and related problems,” Journal of Mathematical Analysis and Applications, vol. 391, no. 2, pp. 350–362, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus