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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 574356, 10 pages
http://dx.doi.org/10.1155/2013/574356
Research Article

Global Exponential Stability of a Unique Almost Periodic Solution for Neutral-Type Cohen-Grossberg Neural Networks with Time Delays

1School of Mathematics and Computer Science, Panzhihua University, Panzhihua, Sichuan 617000, China
2Department of Mathematics, ABa Teacher's College, Wenchuan, Sichuan 623002, China
3City College, Kunming University of Science and Technology, Kunming 650051, China

Received 11 July 2013; Accepted 23 August 2013

Academic Editor: Yong-Kui Chang

Copyright © 2013 Yongzhi Liao 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. M. A. Cohen and S. Grossberg, “Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 13, no. 5, pp. 815–826, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Z. Zeng and J. Wang, “Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli,” Neural Networks, vol. 19, no. 10, pp. 1528–1537, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. Z. Huang, S. Mohamad, and G. Cai, “2N almost periodic attractors for CNNs with variable and distributed delays,” Journal of the Franklin Institute, vol. 346, no. 4, pp. 391–412, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Z. Huang, S. Mohamad, X. Wang, and C. Feng, “Convergence analysis of general neural networks under almost periodic stimuli,” International Journal of Circuit Theory and Applications, vol. 37, no. 6, pp. 723–750, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. 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
  6. Y. Li, “Existence and stability of periodic solutions for Cohen-Grossberg neural networks with multiple delays,” Chaos, Solitons and Fractals, vol. 20, no. 3, pp. 459–466, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C. Wu, J. Ruan, and W. Lin, “On the existence and stability of the periodic solution in the Cohen-Grossberg neural network with time delay and high-order terms,” Applied Mathematics and Computation, vol. 177, no. 1, pp. 194–210, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. B. Liu and L. Huang, “Existence and exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with time-varying delays,” Chaos, Solitons and Fractals, vol. 32, no. 2, pp. 617–627, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. F. Long, Y. Wang, and S. Zhou, “Existence and exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with bounded and unbounded delays,” Nonlinear Analysis: Real World Applications, vol. 8, no. 3, pp. 797–810, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. B. Li and D. Xu, “Existence and exponential stability of periodic solution for impulsive Cohen-Grossberg neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 219, no. 5, pp. 2506–2520, 2012. View at Publisher · View at Google Scholar
  11. Y. Li, X. Chen, and L. Zhao, “Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales,” Neurocomputing, vol. 72, no. 7–9, pp. 1621–1630, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. X. Yang, “Existence and global exponential stability of periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks with delays and impulses,” Neurocomputing, vol. 72, no. 10–12, pp. 2219–2226, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Li and X. Fan, “Existence and globally exponential stability of almost periodic solution for Cohen-Grossberg BAM neural networks with variable coefficients,” Applied Mathematical Modelling, vol. 33, no. 4, pp. 2114–2120, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. Li, T. Zhang, and Z. Xing, “The existence of nonzero almost periodic solution for Cohen-Grossberg neural networks with continuously distributed delays and impulses,” Neurocomputing, vol. 73, no. 16–18, pp. 3105–3113, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. 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
  16. Z. Zhang, G. Peng, and D. Zhou, “Periodic solution to Cohen-Grossberg BAM neural networks with delays on time scales,” Journal of the Franklin Institute, vol. 348, no. 10, pp. 2759–2781, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. 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
  18. H. Xiang, J. Wang, and J. Cao, “Almost periodic solution to Cohen-Grossberg-type BAM networks with distributed delays,” Neurocomputing, vol. 72, no. 16–18, pp. 3751–3759, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. Zhang, L. Guo, and C. Feng, “Stability analysis on a neutral neural network model,” in Advances in Intelligent Computing, D.-S. Huang, X.-P. Zhang, and G.-B. Huang, Eds., vol. 3644 of Lecture Notes in Computer Science, pp. 697–706, 2005. View at Publisher · View at Google Scholar
  20. S. Mandal and N. C. Majee, “Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays,” Neurocomputing, vol. 74, no. 6, pp. 1000–1007, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. Z. Zhang, W. Liu, and D. Zhou, “Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays,” Neural Networks, vol. 25, pp. 94–105, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. V. Covachev, H. Akça, and M. Sarr, “Discrete-time counterparts of impulsive Cohen-Grossberg neural networks of neutral type,” Neural, Parallel and Scientific Computations, vol. 19, no. 3-4, pp. 345–359, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. C. Bai, “Periodic oscillation for Cohen-Grossberg-type bidirectional associative memory neural networks with neutral time-varying delays,” in Proceedings of the 5th International Conference on Natural Computation (ICNC '09), vol. 2, pp. 18–23, Tianjin, China, August 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. C.-D. Zheng, J.-W. Li, and Z. Wang, “New stability criteria for neutral-type Cohen-Grossberg neural networks with discrete and distributed delays,” International Journal of Computer Mathematics, vol. 89, no. 4, pp. 443–466, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. A. M. Fink, Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974. View at MathSciNet
  26. M. Altman, “A fixed point theorem in Hilbert space,” Bulletin of the Polish Academy of Sciences, vol. 5, pp. 19–22, 1957. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. D. J. Guo, Nonlinear Functional Analysis, Shandong Science and Technology Press, Shandong, China, 2003, (Chinese).
  28. 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 Zentralblatt MATH · View at MathSciNet
  29. H. Zhao, L. Chen, and Z. Mao, “Existence and stability of almost periodic solution for Cohen-Grossberg neural networks with variable coefficients,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 663–673, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. Z. Chen, D. Zhao, and J. Ruan, “Almost periodic attractor for Cohen-Grossberg neural networks with delay,” Physics Letters A, vol. 373, no. 4, pp. 434–440, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet