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Journal of Applied Mathematics
Volume 2012, Article ID 523812, 12 pages
http://dx.doi.org/10.1155/2012/523812
Research Article

LMI Approach to Stability Analysis of Cohen-Grossberg Neural Networks with -Laplace Diffusion

1Department of Mathematics, Yibin University, Yibin 644007, China
2Institute of Mathematics, Yibin University, Yibin 644007, China
3College of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China

Received 1 August 2012; Revised 24 October 2012; Accepted 12 November 2012

Academic Editor: Zhilong L. Huang

Copyright © 2012 Xiongrui Wang 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
  2. K. Yuan and J. Cao, “An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis,” IEEE Transactions on Circuits and Systems I, vol. 52, no. 9, pp. 1854–1861, 2005. View at Publisher · View at Google Scholar
  3. S. Arik and Z. Orman, “Global stability analysis of Cohen-Grossberg neural networks with time varying delays,” Physics Letters A, vol. 341, no. 5-6, pp. 410–421, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. J. Zhang, Y. Suda, and H. Komine, “Global exponential stability of Cohen-Grossberg neural networks with variable delays,” Physics Letters A, vol. 338, no. 1, pp. 44–50, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. X. H. Zhang, S. L. 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
  6. M. Jiang, Y. Shen, and X. Liao, “Boundedness and global exponential stability for generalized Cohen-Grossberg neural networks with variable delay,” Applied Mathematics and Computation, vol. 172, no. 1, pp. 379–393, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Q. Song and J. Cao, “Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays,” Journal of Computational and Applied Mathematics, vol. 197, no. 1, pp. 188–203, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. K. N. Wu and X. H. Ding, “Stability and stabilization of impulsive stochastic delay differential equations,” Mathematical Problems in Engineering, vol. 2012, Article ID 176375, 16 pages, 2012. View at Publisher · View at Google Scholar
  9. Y. F. Guo and F. L. Zhu, “New results on stability and stabilization of markovian jump systems with partly known transition probabilities,” Mathematical Problems in Engineering, vol. 2012, Article ID 869842, 11 pages, 2012. View at Google Scholar
  10. K. Wang, Z. D. Teng, and H. J. Jiang, “Global exponential synchronization in delayed reaction-diffusion cellular neural networks with the Dirichlet boundary conditions,” Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 12–24, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. J. Cao and J. Wang, “Global asymptotic stability of a general class of recurrent neural networks with time-varying delays,” IEEE Transactions on Circuits and Systems I, vol. 50, no. 1, pp. 34–44, 2003. View at Publisher · View at Google Scholar
  12. P. Balasubramaniam and R. Rakkiyappan, “Delay-dependent robust stability analysis for Markovian jumping stochastic Cohen-Grossberg neural networks with discrete interval and distributed time-varying delays,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 3, pp. 207–214, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. R. Rakkiyappan and P. Balasubramaniam, “Dynamic analysis of Markovian jumping impulsive stochastic Cohen-Grossberg neural networks with discrete interval and distributed time-varying delays,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 4, pp. 408–417, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. M. Syed Ali and P. Balasubramaniam, “Robust stability of uncertain fuzzy Cohen-Grossberg BAM neural networks with time-varying delays,” Expert Systems with Applications, vol. 36, no. 7, pp. 10583–10588, 2009. View at Publisher · View at Google Scholar
  15. X. Liang and L. S. Wang, “Exponential stability for a class of stochastic reaction-diffusion Hopfield neural networks with delays,” Journal of Applied Mathematics, Article ID 693163, 12 pages, 2012. View at Google Scholar · View at Zentralblatt MATH
  16. Y. T. Zhang, “Asymptotic stability of impulsive reaction-diffusion cellular neural networks with time-varying delays,” Journal of Applied Mathematics, Article ID 501891, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. A. Salem, “Invariant regions and global existence of solutions for reaction-diffusion systems with a tridiagonal matrix of diffusion coefficients and nonhomogeneous boundary conditions,” Journal of Applied Mathematics, Article ID 12375, 15 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. P. Balasubramaniam and C. Vidhya, “Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction-diffusion terms,” Journal of Computational and Applied Mathematics, vol. 234, no. 12, pp. 3458–3466, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. D. J. Higham and T. Sardar, “Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay,” Applied Numerical Mathematics, vol. 18, no. 1–3, pp. 155–173, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. R. F. Rao, S. M. Zhong, and X. R. Wang, “Stochastic stability criteria with LMI conditions for Markovian jumping impulsive BAM neural networks with mode-dependent time-varying delays and nonlinear reaction-diffusion,” Communications in Nonlinear Science and Numerical Simulation. In press.
  21. D. Yue, S. F. Xu, and Y. Q. Liu, “A differential inequality with delay and impulse and its applications to the design of robust controllers,” Control Theory & Applications, vol. 16, no. 4, pp. 519–524, 1999. View at Google Scholar
  22. X. H. Wang, Q. Y. Guo, and D. Y. Xu, “Exponential p-stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,” Mathematics and Computers in Simulation, vol. 79, no. 5, pp. 1698–1710, 2009. View at Publisher · View at Google Scholar