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Mathematical Problems in Engineering
Volume 2015, Article ID 140857, 8 pages
http://dx.doi.org/10.1155/2015/140857
Research Article

Input-to-State Stability of Stochastic Memristive Neural Networks with Time-Varying Delay

Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China

Received 24 September 2014; Accepted 10 January 2015

Academic Editor: Nazim I. Mahmudov

Copyright © 2015 Xu Y. Lou and Qian Ye. 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. L. D. Wang, M. T. Duan, and S. K. Duan, “Memristive chebyshev neural network and its applications in function approximation,” Mathematical Problems in Engineering, vol. 2013, Article ID 429402, 7 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  2. Y. V. Pershin and M. Di Ventra, “Experimental demonstration of associative memory with memristive neural networks,” Neural Networks, vol. 23, no. 7, pp. 881–886, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. G. D. Zhang and Y. Shen, “Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control,” Neural Networks, vol. 55, pp. 1–10, 2014. View at Publisher · View at Google Scholar · View at Scopus
  4. L. D. Wang, M. T. Duan, S. K. Duan, and X. F. Hu, “Neural networks based on STDP rules and memristor bridge synapses with applications in image processing,” Science China: Information Sciences, vol. 44, no. 7, pp. 920–930, 2014. View at Google Scholar
  5. G. D. Zhang, Y. Shen, and J. W. Sun, “Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays,” Neurocomputing, vol. 97, pp. 149–154, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Li, M. Hu, and L. Guo, “Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays,” Neurocomputing, vol. 138, pp. 92–98, 2014. View at Publisher · View at Google Scholar · View at Scopus
  7. Z. Y. Guo, J. Wang, and Z. Yan, “Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays,” Neural Networks, vol. 48, pp. 158–172, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. X. Wang, C. D. Li, and T. W. Huang, “Delay-dependent robust stability and stabilization of uncertain memristive delay neural networks,” Neurocomputing, vol. 140, pp. 155–161, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Wu and Z. G. Zeng, “Improved conditions for global exponential stability of a generalclass of memristive neural networks,” Communications in Nonlinear Science and Numerical Simulation, vol. 20, no. 3, pp. 975–985, 2015. View at Publisher · View at Google Scholar
  10. S. Haykin, Neural Networks, Prentice-Hall, Upper Saddle River, NJ, USA, 1994.
  11. Q. Zhu and J. D. Cao, “Mean-square exponential input-to-state stability of stochastic delayed neural networks,” Neurocomputing, vol. 131, pp. 157–163, 2014. View at Publisher · View at Google Scholar · View at Scopus
  12. E. D. Sontag, “On the input-to-state stability property,” European Journal of Control, vol. 1, no. 1, pp. 24–36, 1995. View at Publisher · View at Google Scholar · View at Scopus
  13. E. N. Sanchez and J. P. Perez, “Input-to-state stability (ISS) analysis for dynamic neural networks,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 46, no. 11, pp. 1395–1398, 1999. View at Publisher · View at Google Scholar · View at Scopus
  14. S. P. Wen, Z. G. Zeng, and T. W. 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
  15. S. P. Wen, Z. G. Zeng, and T. W. 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
  16. J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, Mass, USA, 2009.
  17. A. F. Filippov, “Classical solutions of differential equations with multi-valued right-hand side,” SIAM Journal on Control, vol. 5, no. 4, pp. 609–621, 1967. View at Publisher · View at Google Scholar
  18. X. R. Mao, Stochastic Differential Equations and Applications, Horwood Publishing, Chichester, UK, 2nd edition, 2007.
  19. I. E. Ebong and P. Mazumder, “CMOS and memristor-based neural network design for position detection,” Proceedings of the IEEE, vol. 100, no. 6, pp. 2050–2060, 2012. View at Publisher · View at Google Scholar · View at Scopus