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Stability in the numerical simulation of stochastic delayed Hopfield neural networks

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Abstract

This paper is concerned with the mean-square stability of the Split-Step Backward Euler method for stochastic delayed Hopfield neural networks. The sufficient conditions to guarantee the mean-square stability of the Split-Step Backward Euler method are given. Moreover, an example of the comparison of our method with the Euler–Maruyama method is used to show the superiority of our method.

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References

  1. Venetianer P, Roska T (1998) Image compression by delayed CNNs. IEEE Trans Circuits Syst I 45:205–215

    Article  Google Scholar 

  2. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci (Biophysics) 79:2554–2558

    Article  MathSciNet  Google Scholar 

  3. Forti M, Tesi A (1995) New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans Circuits Syst I, Fundam Theory Appl 42(7):354–366

    Article  MathSciNet  MATH  Google Scholar 

  4. Zeng Z, Huang D, Wang Z (2005) Memory pattern analysis of cellular neural networks. Phys Lett A 342:114–128

    Article  MATH  Google Scholar 

  5. Luo L, Zeng Z, Liao X (2011) Global exponential stability in Lagrange sense for neutral type recurrent neural networks. Neurocomputing 74(4):638–645

    Article  Google Scholar 

  6. Shen Y, Wang J (2008) An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying Delays. IEEE Trans Neural Netw 19(3):528–531

    Article  Google Scholar 

  7. Shen Y, Wang J (2009) Almost sure exponential stability of recurrent neural networks with Markovian switching. IEEE Trans Neural Netw Reg paper 20(5):840–855

    Article  MathSciNet  Google Scholar 

  8. Liu M (2008) Global asymptotic stability analysis of discrete-time Cohen-Grossberg neural networks based on interval systems. Nonlinear Anal Theory Methods Appl 69(8):2403–2411

    Article  MATH  Google Scholar 

  9. Cao J, Wang J (2003) Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans Circuits Syst I 50(1):34–44

    Article  MathSciNet  Google Scholar 

  10. Xu S, Lam J, Ho DWC (2006) A new LMI condition for delay dependent asymptotic stability of delayed Hopfield neural networks. IEEE Trans Circuits Syst II Exp Briefs 53(3):230–234

    Article  Google Scholar 

  11. Chen T, Amari S (2001) Stability of asymmetric Hopfield networks. IEEE Trans Neural Netw 12:159–163

    Article  Google Scholar 

  12. Huang C, Chen P, He Y, Huang L, Tan W (2008) Almost sure exponential stability of delayed Hopfield neural networks. Appl Math Lett 21:701–705

    Article  MathSciNet  MATH  Google Scholar 

  13. Wan L, Sun J (2005) Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys Lett A 343:306–318

    Article  MATH  Google Scholar 

  14. Zhou Q, Wan L (2008) Exponential stability of stochastic delayed Hopfield neural networks. Appl Math Comput 199:84–89

    Article  MathSciNet  MATH  Google Scholar 

  15. Li R, Pang W, Leung P (2010) Exponential stability of numerical solutions to stochastic delay Hopfield neural networks. Neurocomputing 73:920–926

    Article  MATH  Google Scholar 

  16. Mao X (2007) Stochastic differential equations and applications, 2nd edn. Horwood, Chichester

    MATH  Google Scholar 

  17. Küchler U, Platen E (2000) Strong discrete time approximation of stochastic differential equations with time delay. Math Comput Simulat 54:189–205

    Article  Google Scholar 

  18. Higham DJ, Mao X, Stuart AM (2002) Strong convergence of Euler-type methods for nonlinear stochastic differential equations. SIAM J Numer Anal 40(3):1041–1063

    Article  MathSciNet  MATH  Google Scholar 

  19. Jiang F, Shen Y, Wu F (2011) Convergence of numerical approximation for jump models involving delay and mean-reverting square root process. Stoch Anal Appl 29:216–236

    Article  MathSciNet  MATH  Google Scholar 

  20. Jiang F, Shen Y, Hu J (2011) Stability of the split-step backward Euler scheme for stochastic delay integro-differential equations with Markovian switching. Commun Nonlinear Sci Numer Simulat 16:814–821

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The work was supported by the State Key Program of National Natural Science of China (Grant No. 61134012), the Fundamental Research Funds for the Central Universities (2012089) and Zhongnan University Economics and Law.

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, China

    Feng Jiang

  2. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Feng Jiang

  3. Department of Control Science and Engineering and the Key Laboratory of Ministry of Eduction for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yi Shen

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  1. Feng Jiang
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  2. Yi Shen
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Correspondence to Feng Jiang.

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Jiang, F., Shen, Y. Stability in the numerical simulation of stochastic delayed Hopfield neural networks. Neural Comput & Applic 22, 1493–1498 (2013). https://doi.org/10.1007/s00521-012-0935-0

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  • DOI: https://doi.org/10.1007/s00521-012-0935-0

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