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Journal of Applied Mathematics
Volume 2014, Article ID 705496, 8 pages
http://dx.doi.org/10.1155/2014/705496
Research Article

Global Exponential Robust Stability of High-Order Hopfield Neural Networks with S-Type Distributed Time Delays

1College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China
2School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
3College of Marine Life Science and School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China

Received 24 March 2014; Accepted 1 June 2014; Published 26 June 2014

Academic Editor: Reinaldo Martinez Palhares

Copyright © 2014 Haiyong Zheng 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. S. Wen, Z. Zeng, T. Huang, and Y. Zhang, “Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudo random number generators,” IEEE Transactions on Fuzzy Systems, 2013. View at Publisher · View at Google Scholar
  2. J. Cao, G. Chen, and P. Li, “Global synchronization in an array of delayed neural networks with hybrid coupling,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 38, no. 2, pp. 488–498, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Cao and M. Xiao, “Stability and Hopf bifurcation in a simplified BAM neural network with two time delays,” IEEE Transactions on Neural Networks, vol. 18, no. 2, pp. 416–430, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Wen, G. Bao, Z. Zeng, Y. Chen, and T. Huang, “Global exponential synchronization of memristor-based recurrent networks with time-varying delays,” Neural Networks, vol. 48, pp. 195–203, 2013. View at Google Scholar
  5. S. Wen, Z. Zeng, and T. Huang, “Associative learning of integrate-and-fire neurons with memristor-based synapses,” Neural Processing Letters, vol. 38, no. 1, pp. 69–80, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. G. Wallis, “Stability criteria for unsupervised temporal association networks,” IEEE Transactions on Neural Networks, vol. 16, no. 2, pp. 301–311, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. C. Wang and D. J. Hill, “Deterministic learning and rapid dynamical pattern recognition,” IEEE Transactions on Neural Networks, vol. 18, no. 3, pp. 617–630, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. X. Liao and Y. Liao, “Stability of Hopfield-type neural networks II,” Science in China A, vol. 40, no. 8, pp. 813–816, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  9. K. Gopalsamy and X. Z. He, “Stability in asymmetric Hopfield nets with transmission delays,” Physica D: Nonlinear Phenomena, vol. 76, no. 4, pp. 344–358, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. D. Xu, H. Zhao, and H. Zhu, “Global dynamics of hopfield neural networks involving variable delays,” Computers & Mathematics with Applications, vol. 42, no. 1-2, pp. 39–45, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. Wang, P. Lin, and L. Wang, “Exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 13, no. 3, pp. 1353–1361, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Y. Wang, C. Lu, G. Ji, and L. Wang, “Global exponential stability of high-order Hopfield-type neural networks with S-type distributed time delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 3319–3325, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proceedings of the National Academy of Sciences of the United States of America, vol. 79, no. 8, pp. 2554–2558, 1982. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons,” Proceedings of the National Academy of Sciences of the United States of America, vol. 81, no. 10, pp. 3088–3092, 1984. View at Publisher · View at Google Scholar · View at Scopus
  15. L. Wang, Delayed Recurrent Neural Networks, Science Press, Beijing, China, 2008.
  16. P. P. Civalleri, M. Gilli, and L. Pandolfi, “On stability of cellular neural networks with delay,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 40, no. 3, pp. 157–165, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. S. Wen, Z. Zeng, and T. Huang, “H∞ filtering for neutral systems with mixed delays and multiplicative noises,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 59, no. 11, pp. 820–824, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Wen, Z. Zeng, and T. Huang, “Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays,” Neurocomputing, vol. 97, pp. 233–240, 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Wen, Z. Zeng, T. Huang, and C. Li, “Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays,” International Journal o f Robust and Nonlinear Control, 2013. View at Publisher · View at Google Scholar
  20. X. Liao, Y. Fu, J. Gao, and X. Zhao, “Stability of Hopfield neural networks with reaction-diffusion terms,” Acta Electronica Sinica, vol. 28, no. 1, pp. 78–80, 2000. View at Google Scholar · View at Scopus
  21. Q. Song, Z. Zhao, and Y. Li, “Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms,” Physics Letters A: General, Atomic and Solid State Physics, vol. 335, no. 2-3, pp. 213–225, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. L. Wang and Y. Gao, “Global exponential robust stability of reaction-diffusion interval neural networks with time-varying delays,” Physics Letters. A, vol. 350, no. 5-6, pp. 342–348, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. L. Wang and D. Xu, “Asymptotic behavior of a class of reaction-diffusion equations with delays,” Journal of Mathematical Analysis and Applications, vol. 281, no. 2, pp. 439–453, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. S. Ruan and R. S. Filfil, “Dynamics of a two-neuron system with discrete and distributed delays,” Physica D: Nonlinear Phenomena, vol. 191, no. 3-4, pp. 323–342, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. J. Cao, K. Yuan, and H. Li, “Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays,” IEEE Transactions on Neural Networks, vol. 17, no. 6, pp. 1646–1651, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. L. Wang and D. Xu, “Global asymptotic stability of bidirectional associative memory neural networks with S-type distributed delays,” International Journal of Systems Science, vol. 33, no. 11, pp. 869–877, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. P. Liu, F. Yi, Q. Guo, J. Yang, and W. Wu, “Analysis on global exponential robust stability of reaction-diffusion neural networks with S-type distributed delays,” Physica D: Nonlinear Phenomena, vol. 237, no. 4, pp. 475–485, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. L. Wang, R. Zhang, and Y. Wang, “Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 1101–1113, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. W. Han, Y. Kao, and L. Wang, “Global exponential robust stability of static interval neural networks with S-type distributed delays,” Journal of the Franklin Institute, vol. 348, no. 8, pp. 2072–2081, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. X. Liu and Q. Wang, “Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 1, pp. 71–79, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. 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 Scopus
  32. M. Brucoli, L. Carnimeo, and G. Grassi, “Associative memory design using discrete-time second-order neural networks with local interconnections,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 44, no. 2, pp. 153–158, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  33. 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
  34. A. Dembo, O. Farotimi, and T. Kailath, “High-order absolutely stable neural networks,” IEEE transactions on circuits and systems, vol. 38, no. 1, pp. 57–65, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  35. S. Hu, Nonlinear Analysis and Methods, Huazhong University of Sci ence and Technology Press, Wuhan, China, 1993.
  36. D. Guo, J. Sun, and Z. Liu, Functional Methods of Nonlinear Ordinary Differential Equations, Shandong Science Press, Jinan, China, 1995.
  37. X. Liao, G. Chen, and E. N. Sanchez, “L{MI}-based approach for asymptotically stability analysis of delayed neural networks,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 49, no. 7, pp. 1033–1039, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus