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Complexity
Volume 2017, Article ID 6292597, 9 pages
https://doi.org/10.1155/2017/6292597
Research Article

Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory

1Department of Mathematics, Chengdu Normal University, Chengdu 61130, China
2College of Mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China

Correspondence should be addressed to Ruofeng Rao; moc.361@oargnefour

Received 14 July 2017; Accepted 22 August 2017; Published 25 September 2017

Academic Editor: Chenguang Yang

Copyright © 2017 Ruofeng Rao and Shouming Zhong. 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. O. Chua and L. Yang, “Cellular neural networks: theory,” Institute of Electrical and Electronics Engineers. Transactions on Circuits and Systems, vol. 35, no. 10, pp. 1257–1272, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. L. O. Chua and L. Yang, “Cellular neural networks: applications,” Institute of Electrical and Electronics Engineers. Transactions on Circuits and Systems, vol. 35, no. 10, pp. 1273–1290, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. X. Li and R. Rakkiyappan, “Impulse controller design for exponential synchronization of chaotic neural networks with mixed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 6, pp. 1515–1523, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. B. Wang, J. Cheng, and J. Zhan, “A sojourn probability approach to fuzzy-model-based reliable control for switched systems with mode-dependent time-varying delays,” Nonlinear Analysis. Hybrid Systems, vol. 26, pp. 239–253, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  5. X. Li, R. Rakkiyappan, and P. Balasubramaniam, “Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 348, no. 2, pp. 135–155, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. Q. Song, H. Yan, Z. Zhao, and Y. Liu, “Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays,” Neural Networks, vol. 81, pp. 1–10, 2016. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Kimura, R. Morita, S. Sugisaki, T. Matsuda, and Y. Nakashima, “Cellular neural network formed by simplified processing elements composed of thin-film transistors,” Neurocomputing, vol. 248, pp. 112–119, 2017. View at Google Scholar
  8. J. Cheng, J. H. Park, Y. Liu, Z. Liu, and L. Tang, “Finite-time H ∞ fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions,” Fuzzy Sets and Systems, vol. 314, pp. 99–115, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  9. X. Li, C. Ding, and Q. Zhu, “Synchronization of stochastic perturbed chaotic neural networks with mixed delays,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 347, no. 7, pp. 1266–1280, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. B. Wang, J. Cheng, A. Al-Barakati, and H. M. Fardoun, “A mismatched membership function approach to sampled-data stabilization for T-S fuzzy systems with time-varying delayed signals,” Signal Processing, vol. 140, pp. 161–170, 2017. View at Publisher · View at Google Scholar
  11. K. Shi, X. Liu, Y. Tang, H. Zhu, and S. Zhong, “Some novel approaches on state estimation of delayed neural networks,” Information Sciences, vol. 372, pp. 313–331, 2016. View at Publisher · View at Google Scholar · View at Scopus
  12. Q. Song and J. Cao, “Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 345, no. 1, pp. 39–59, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. R. Jia, “Finite-time stability of a class of fuzzy cellular neural networks with multi-proportional delays,” Fuzzy Sets and Systems. An International Journal in Information Science and Engineering, vol. 319, pp. 70–80, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. Y. G. Kao, L. Shi, J. Xie, and H. R. Karimi, “Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability,” Neural Networks, vol. 63, pp. 18–30, 2015. View at Publisher · View at Google Scholar · View at Scopus
  15. B. Liu, “Global exponential stability for BAM neural networks with time-varying delays in the leakage terms,” Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, vol. 14, no. 1, pp. 559–566, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  16. L. Zhou, “Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays,” Neurocomputing, vol. 161, pp. 99–106, 2015. View at Publisher · View at Google Scholar · View at Scopus
  17. J. Luo, “Fixed points and stability of neutral stochastic delay differential equations,” Journal of Mathematical Analysis and Applications, vol. 334, no. 1, pp. 431–440, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. G. Chen, O. van Gaans, and S. Verduyn Lunel, “Fixed points and pth moment exponential stability of stochastic delayed recurrent neural networks with impulses,” Applied Mathematics Letters. An International Journal of Rapid Publication, vol. 27, pp. 36–42, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  19. C. Guo, D. O'Regan, F. Deng, and R. P. Agarwal, “Fixed points and exponential stability for a stochastic neutral cellular neural network,” Applied Mathematics Letters. An International Journal of Rapid Publication, vol. 26, no. 8, pp. 849–853, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  20. X. Yang, Q. Zhu, and Z. Yao, “pth Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations,” Mathematical Problems in Engineering, vol. 2014, Article ID 481246, 7 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  21. R. Rao and Z. Pu, “LMI-based stability criterion of impulsive T-S fuzzy dynamic equations via fixed point theory,” Abstract and Applied Analysis, vol. 2013, Article ID 261353, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. G.-Q. Wang and S. S. Cheng, “Fixed point theorems arising from seeking steady states of neural networks,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 33, no. 1, pp. 499–506, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. Y. Zhang and Q. Luo, “Global exponential stability of impulsive cellular neural networks with time-varying delays via fixed point theory,” Advances in Difference Equations, vol. 2013, 23 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  24. R. Rao, S. Zhong, and Z. Pu, “LMI-based robust exponential stability criterion of impulsive integro-differential equations with uncertain parameters via contraction mapping theory,” Advances in Difference Equations, vol. 2017, 19 pages, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  25. J. Luo, “Exponentially stable stationary solutions for delay stochastic evolution equations,” Progress in Probability, vol. 65, pp. 169–178, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  26. A. A. Kwiecinska, “Stabilization of partial differential equations by noise,” Stochastic Processes and their Applications, vol. 79, no. 2, pp. 179–184, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  27. R. Rao and Z. Pu, “Stability analysis for impulsive stochastic fuzzy p-Laplace dynamic equations under Neumann or Dirichlet boundary condition,” Boundary Value Problems, vol. 2013, 14 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  28. Q. Zhu, X. Li, and X. Yang, “Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays,” Applied Mathematics and Computation, vol. 217, no. 13, pp. 6078–6091, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  29. R. Rao, S. Zhong, and Z. Pu, “On the role of diffusion factors in stability analysis for p-Laplace dynamical equations involved to BAM Cohen-Grossberg neural network,” Neurocomputing, vol. 223, pp. 54–62, 2017. View at Publisher · View at Google Scholar
  30. B. Xie, “The moment and almost surely exponential stability of stochastic heat equations,” Proceedings of the American Mathematical Society, vol. 136, no. 10, pp. 3627–3634, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. X. Li and F. Deng, “Razumikhin method for impulsive functional differential equations of neutral type,” Chaos, Solitons & Fractals, vol. 101, pp. 41–49, 2017. View at Publisher · View at Google Scholar · View at MathSciNet