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Stability of Stochastic \(\theta \)-Methods for Stochastic Delay Hopfield Neural Networks Under Regime Switching

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Abstract

This paper is concerned with the general mean-square (GMS) stability and mean-square (MS) stability of stochastic \(\theta \)-methods for stochastic delay Hopfield neural networks under regime switching. The sufficient conditions to guarantee GMS-stability and MS-stability of stochastic \(\theta \)-methods are given. Finally, an example is used to illustrate the effectiveness of our result.

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References

  1. 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 

  2. 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 

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

    Article  Google Scholar 

  4. Jiang M, Shen Y, Liao X (2006) Boundedness and global exponential stability for generalized Cohen-Grosssberg neural networks with variale delay. Appl Math Comput 172:379–393

    Article  MathSciNet  MATH  Google Scholar 

  5. Wen S, Zeng Z (2012) Dynamics analysis of a class of memristor-based recurrent networks with time-varying delays in the presence of strong external stimuli. Neural Process Lett 35:47–59

    Article  Google Scholar 

  6. Chen H, Zhang Y, Hu P (2010) Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks. Neurocomputing 73:2554–2561

    Article  Google Scholar 

  7. Chen G, Shen Y, Zhu S (2011) Non-fragile observer-based \(\text{ H}_\infty \) control for neutral stochastic hybrid systems with time-varying delay. Neural Comput Appl 20:1149–1158

    Article  Google Scholar 

  8. Mahmoud MS, Shi P (2003) Robust stability, stabilization and \(\text{ H}_\infty \) control of time-delay systems with Markovian jump parameters. Int. J. Robust Nonlinear Control 13:755–784

    Article  MathSciNet  MATH  Google Scholar 

  9. Lou X, Cui B (2009) Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters. Chaos Solitons Fractals 39:2188–2197

    Article  MathSciNet  MATH  Google Scholar 

  10. Huang H, Ho DWC, Qu Y (2007) Robust stability of stochastic delayed additive neural networks with Markovian switching. Neural Netw 20:799–809

    Article  MATH  Google Scholar 

  11. Chen W, Xu J, Guan Z (2003) Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays. IEEE Trans Autom Control 48:2270–2277

    Article  MathSciNet  Google Scholar 

  12. Zhu S, Shen Y, Liu L (2010) Exponential stability of uncertain stochastic neural networks with Markovian switching. Neural Process Lett 32:293–309

    Article  Google Scholar 

  13. Mao X, Yuan C (2006) Stochastic differential equations with Markovian switching. Imperial College Press, London

    Book  MATH  Google Scholar 

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

    Article  Google Scholar 

  15. 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 

  16. Hu P, Huang C (2011) Stability of stochastic \(\theta \)-methods for stochastic delay integro-differential equations. Int J Comput Math 88:1417–1429

    Article  MathSciNet  MATH  Google Scholar 

  17. 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 Simul 16:814–821

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhou S, Wu F (2009) Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching. J Comput Appl Math 229:85–96

    Article  MathSciNet  MATH  Google Scholar 

  19. 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 

  20. Jiang F, Shen Y, (2012) Stability in the numerical simulation of stochastic delayed Hopfield neural networks. Neural Comput Applic. doi:10.1007/s00521-012-0935-0

Download references

Acknowledgments

The work is supported by the Fundamental Research Funds for the Central Universities, China Postdoctoral Science Foundation funded project under Grant 2012M511615 and the State Key Program of National Natural Science of China under Grant 61134012.

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Authors and Affiliations

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

    Feng Jiang

  2. Department of Control Science and Engineering, 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 of Stochastic \(\theta \)-Methods for Stochastic Delay Hopfield Neural Networks Under Regime Switching. Neural Process Lett 38, 433–444 (2013). https://doi.org/10.1007/s11063-013-9284-y

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  • DOI: https://doi.org/10.1007/s11063-013-9284-y

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