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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 963897, 10 pages
http://dx.doi.org/10.1155/2013/963897
Research Article

Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 28 June 2013; Accepted 30 September 2013

Academic Editor: Xiang Ping Yan

Copyright © 2013 Yanke Du and Rui Xu. 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. W. Han, Y. Liu, and L. Wang, “Robust exponential stability of Markovian jumping neural networks with mode-dependent delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2529–2535, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. O. M. Kwon, S. M. Lee, and J. H. Park, “Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays,” Physics Letters A, vol. 374, no. 10, pp. 1232–1241, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. X. Li, “Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4370–4384, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J.-L. Shao, T.-Z. Huang, and X.-P. Wang, “Improved global robust exponential stability criteria for interval neural networks with time-varying delays,” Expert Systems with Applications, vol. 38, no. 12, pp. 15587–15593, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. J.-L. Shao, T.-Z. Huang, and S. Zhou, “An analysis on global robust exponential stability of neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 7–9, pp. 1993–1998, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. J.-L. Shao, T.-Z. Huang, and S. Zhou, “Some improved criteria for global robust exponential stability of neural networks with time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 3782–3794, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. F. Wang and H. Wu, “Mean square exponential stability and periodic solutions of stochastic interval neural networks with mixed time delays,” Neurocomputing, vol. 73, no. 16–18, pp. 3256–3263, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. W. Zhao and Q. Zhu, “New results of global robust exponential stability of neural networks with delays,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 1190–1197, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Liu, Y. Oua, J. Hu, et al., “Delay-dependent stability analysis for continuous-time BAM neural networks with Markovian jumping parameters,” Neural Networks, vol. 23, pp. 315–321, 2010.
  10. J. Pan, X. Liu, and S. Zhong, “Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays,” Mathematical and Computer Modelling, vol. 51, no. 9-10, pp. 1037–1050, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Tian and S. Zhong, “Improved delay-dependent stability criterion for neural networks with time-varying delay,” Applied Mathematics and Computation, vol. 217, no. 24, pp. 10278–10288, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. Wang, Q. Song, and C. Duan, “LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions,” Mathematics and Computers in Simulation, vol. 81, no. 4, pp. 837–850, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. Zhang, S. Wu, and K. Li, “Delay-dependent exponential stability for impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1524–1532, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. X. Fu and X. Li, “LMI conditions for stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 435–454, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. K. Li, “Stability analysis for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 2784–2798, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. B. Zhou, Q. Song, and H. Wang, “Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales,” Neurocomputing, vol. 74, no. 17, pp. 3142–3150, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. P. Balasubramaniam and M. S. Ali, “Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays,” Fuzzy Sets and Systems, vol. 161, no. 4, pp. 608–618, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. W. Su and Y. Chen, “Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 520–528, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Z. Wang, H. Zhang, and W. Yu, “Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay,” Neurocomputing, vol. 72, no. 4–6, pp. 1105–1110, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. Z. Huang and Y. Xia, “Exponential periodic attractor of impulsive BAM networks with finite distributed delays,” Chaos, Solitons & Fractals, vol. 39, no. 1, pp. 373–384, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. Townley, A. Ilchmann, M. G. Weiss et al., “Existence and learning of oscillations in recurrent neural networks,” IEEE Transactions on Neural Networks, vol. 11, no. 1, pp. 205–214, 2000. View at Publisher · View at Google Scholar · View at Scopus
  22. X. Chen and Q. Song, “Global exponential stability of the periodic solution of delayed Cohen-Grossberg neural networks with discontinuous activations,” Neurocomputing, vol. 73, no. 16–18, pp. 3097–3104, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. C.-H. Li and S.-Y. Yang, “Existence and attractivity of periodic solutions to non-autonomous Cohen-Grossberg neural networks with time delays,” Chaos, Solitons and Fractals, vol. 41, no. 3, pp. 1235–1244, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Q. Liu and R. Xu, “Periodic solutions of high-order Cohen-Grossberg neural networks with distributed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2887–2893, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. J. Pan and Y. Zhan, “On periodic solutions to a class of non-autonomously delayed reaction-diffusion neural networks,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 414–422, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. H. Xiang and J. Cao, “Exponential stability of periodic solution to Cohen-Grossberg-type BAM networks with time-varying delays,” Neurocomputing, vol. 72, no. 7–9, pp. 1702–1711, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. Q. Liu and R. Xu, “Periodic solutions of a Cohen-Grossberg-type BAM neural networks with distributed delays and impulses,” Journal of Applied Mathematics, vol. 2012, Article ID 643418, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. J. C. Principe, J.-M. Kuo, and S. Celebi, “An analysis of the gamma memory in dynamics neural networks,” IEEE Transactions on Neural Networks, vol. 5, no. 2, pp. 331–337, 1994. View at Publisher · View at Google Scholar · View at Scopus
  29. J. Zhang, “Global exponential stability of interval neural networks with variable delays,” Applied Mathematics Letters, vol. 19, no. 11, pp. 1222–1227, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, Mass, USA, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  31. H. Zhang, Z. Wang, and D. Liu, “Robust exponential stability of recurrent neural networks with multiple time-varying delays,” IEEE Transactions on Circuits and Systems II, vol. 54, no. 8, pp. 730–734, 2007. View at Publisher · View at Google Scholar · View at Scopus
  32. Y. Du and R. Xu, “Global robust exponential stability analysis for interval neural networks with mixed delays,” Abstract and Applied Analysis, vol. 2012, Article ID 647231, 18 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. T. Ensari and S. Arik, “New results for robust stability of dynamical neural networks with discrete time delays,” Expert Systems with Applications, vol. 37, no. 8, pp. 5925–5930, 2010. View at Publisher · View at Google Scholar · View at Scopus
  34. N. Ozcan and S. Arik, “Global robust stability analysis of neural networks with multiple time delays,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 1, pp. 166–176, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  35. V. Singh, “Improved global robust stability criterion for delayed neural networks,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 224–229, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet