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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 236562, 21 pages
http://dx.doi.org/10.1155/2012/236562
Research Article

Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays

1School of Science, Xidian University, Xi'an 710071, China
2Institute of Math and Applied Math, Xianyang Normal University, Xianyang 712000, China

Received 17 April 2012; Accepted 16 June 2012

Academic Editor: Sabri Arik

Copyright © 2012 Weiyuan Zhang 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. Y. Zheng and T. Chen, “Global exponential stability of delayed periodic dynamical systems,” Physics Letters A, vol. 322, no. 5-6, pp. 344–355, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. J. Cao and J. Wang, “Global exponential stability and periodicity of recurrent neural networks with time delays,” IEEE Transactions on Circuits and Systems I, vol. 52, no. 5, pp. 920–931, 2005. View at Publisher · View at Google Scholar
  3. 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
  4. X. Li, “Existence and global exponential stability of periodic solution for delayed neural networks with impulsive and stochastic effects,” Neurocomputing, vol. 73, no. 4–6, pp. 749–758, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. S. M. Lee, O. M. Kwon, and J. H. Park, “A novel delay-dependent criterion for delayed neural networks of neutral type,” Physics Letters A, vol. 374, no. 17-18, pp. 1843–1848, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. C. Huang and J. Cao, “Convergence dynamics of stochastic Cohen-Grossberg neural networks with unbounded distributed delays,” IEEE Transactions on Neural Networks, vol. 22, no. 4, pp. 561–572, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. Q. Zhu and J. Cao, “Stability of Markovian jump neural networks with impulse control and time varying delays,” Nonlinear Analysis: Real World Applications, vol. 13, pp. 2259–2270, 2012. View at Publisher · View at Google Scholar
  8. M. Forti and A. Tesi, “New conditions for global stability of neural networks with application to linear and quadratic programming problems,” IEEE Transactions on Circuits and Systems I, vol. 42, no. 7, pp. 354–366, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. X. G. Liu, R. R. Martin, M. Wu, and M. L. Tang, “Global exponential stability of bidirectional associative memory neural networks with time delays,” IEEE Transactions on Neural Networks, vol. 19, no. 3, pp. 397–407, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. Q. Zhu, C. Huang, and X. Yang, “Exponential stability for stochastic jumping BAM neural networks with time-varying and distributed delays,” Nonlinear Analysis: Hybrid Systems, vol. 5, no. 1, pp. 52–77, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. O. Faydasicok and S. Arik, “Equilibrium and stability analysis of delayed neural networks under parameter uncertainties,” Applied Mathematics and Computation, vol. 218, no. 12, pp. 6716–6726, 2012. View at Publisher · View at Google Scholar
  12. O. Faydasicok and S. Arik, “Further analysis of global robust stability of neural networks with multiple time delays,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 813–825, 2012. View at Publisher · View at Google Scholar
  13. Q. Song, J. Cao, and Z. Zhao, “Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays,” Nonlinear Analysis: Real World Applications, vol. 7, no. 1, pp. 65–80, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. H. Zhao and G. Wang, “Existence of periodic oscillatory solution of reaction-diffusion neural networks with delays,” Physics Letters A, vol. 343, no. 5, pp. 372–383, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. 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
  16. P. Balasubramaniam and C. Vidhya, “Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters,” Expert Systems With Applications, vol. 39, pp. 3109–3115, 2012. View at Publisher · View at Google Scholar
  17. 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
  18. J. Pan and S. Zhong, “Dynamical behaviors of impulsive reaction-diffusion Cohen-Grossberg neural network with delays,” Neurocomputing, vol. 73, no. 7–9, pp. 1344–1351, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. J. G. Lu and L. J. Lu, “Global exponential stability and periodicity of reaction-diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions,” Chaos, Solitons and Fractals, vol. 39, no. 4, pp. 1538–1549, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. J. G. Lu, “Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions,” Chaos, Solitons and Fractals, vol. 35, no. 1, pp. 116–125, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. J. G. Lu, “Robust global exponential stability for interval reaction-diffusion Hopfield neural networks with distributed delays,” IEEE Transactions on Circuits and Systems II, vol. 54, no. 12, pp. 1115–1119, 2007. View at Publisher · View at Google Scholar · View at Scopus
  22. Y. Lv, W. Lv, and J. Sun, “Convergence dynamics of stochastic reaction-diffusion recurrent neural networks in continuously distributed delays,” Nonlinear Analysis: Real World Applications, vol. 9, no. 4, pp. 1590–1606, 2008. View at Publisher · View at Google Scholar
  23. Z. Wang and H. Zhang, “Global asymptotic stability of reaction-diffusion cohen-grossberg neural networks with continuously distributed delays,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 39–49, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. Q. Song and Z. Wang, “Dynamical behaviors of fuzzy reaction-diffusion periodic cellular neural networks with variable coefficients and delays,” Applied Mathematical Modelling, vol. 33, no. 9, pp. 3533–3545, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. C. Hu, H. Jiang, and Z. Teng, “Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 67–81, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. K. Li and Q. Song, “Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms,” Neurocomputing, vol. 72, no. 1–3, pp. 231–240, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. J. Qiu, “Exponential stability of impulsive neural networks with time-varying delays and reaction-diffusion terms,” Neurocomputing, vol. 70, no. 4–6, pp. 1102–1108, 2007. View at Publisher · View at Google Scholar · View at Scopus
  28. L. Wan and Q. Zhou, “Exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays,” Applied Mathematics and Computation, vol. 206, no. 2, pp. 818–824, 2008. View at Publisher · View at Google Scholar
  29. X. Xu, J. Zhang, and W. Zhang, “Mean square exponential stability of stochastic neural networks with reaction-diffusion terms and delays,” Applied Mathematics Letters, vol. 24, no. 1, pp. 5–11, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. 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
  31. W. Zhang, J. Li, and N. Shi, “Stability analysis for stochastic Markovian jump reaction-diffusion neural networks with partially known transition probabilities and mixed time delays,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 524187, 17 pages, 2012. View at Publisher · View at Google Scholar
  32. W. Zhang and J. Li, “Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions,” Boundary Value Problems, vol. 2012, article 2, 2012. View at Publisher · View at Google Scholar
  33. W. Y. Zhang and J. M. Li, “Global exponential stability of reaction—diffusion neural networks with discrete and distributed time-varying delays,” Chinese Physics B, vol. 20, no. 3, Article ID 030701, 2011. View at Publisher · View at Google Scholar · View at Scopus
  34. S. Haykin, Neural Networks, Prentice-Hall, Upper Saddle River, NJ, USA, 1994.
  35. W. Zhu, “Global exponential stability of impulsive reaction-diffusion equation with variable delays,” Applied Mathematics and Computation, vol. 205, no. 1, pp. 362–369, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  36. X.-X. Liao and J. Li, “Stability in Gilpin-Ayala competition models with diffusion,” Nonlinear Analysis: Theory, Methods & Applications, vol. 28, no. 10, pp. 1751–1758, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  37. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Academic, New York, NY, USA, 1969.
  38. J. Liang, Z. Wang, Y. Liu, and X. Liu, “Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 38, no. 4, pp. 1073–1083, 2008. View at Publisher · View at Google Scholar · View at Scopus