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Exponential stability of stochastic high-order BAM neural networks with time delays and impulsive effects

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Abstract

In this paper, we consider the problem on exponential stability analysis of the stochastic impulsive high-order BAM neural networks with time delays. Through employing Lyapunov function method and stochastic bidirected halanay inequality, we constitute exponential stability of the stochastic impulsive high-order BAM neural networks with its estimated exponential convergence rate and feasible interval of impulsive strength. An example illustrates the main results.

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References

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

    Article  MathSciNet  Google Scholar 

  2. Hopfield JJ (1984) Neurons with graded response have collective computational like those of two-state neurons. Proc Natl Acad Sci USA 81:3088–3092

    Article  Google Scholar 

  3. Kosko B (1987) Adaptive bi-directional associative memories. Appl Optim 26:4947–4960

    Article  Google Scholar 

  4. Kosko B (1988) Bidirectional associative memories. IEEE Trans Syst Man Cybernet 18:49–60

    Article  MathSciNet  Google Scholar 

  5. Cao JD, Wang L (2002) Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans Neural Netw 13:457–463

    Article  Google Scholar 

  6. Hu XL, Wang J (2007) Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems. IEEE Trans Syst Man Cybern Part B Cybern 37(5):1414–1421

    Article  Google Scholar 

  7. Ghosh J, Shin Y (1992) Efficient high-order neural networks for classification and function approximation. Int J Neural Syst 3(4):323–350

    Article  Google Scholar 

  8. Liao XF, Wong KW (2004) Robust stability of interval bidirectional associative memory neural network with time delays. IEEE Trans Syst Man Cybern B Cybern 34:1142–1154

    Article  Google Scholar 

  9. Li CD, Liao XF (2005) Delay-dependent exponential stability analysis of bi-directional associative memory neural networks: an LMI approach. Chaos Solitons Fractals 24(4):1119–1134

    Article  MathSciNet  MATH  Google Scholar 

  10. Li CD, Shen YY, Feng G (2008) Stabilizing effects of impulse in delayed BAM neural networks. IEEE Trans Circuits Syst II 53(12):1284–1288

    Article  Google Scholar 

  11. Li CD, Li CJ, Liu C (2009) Destabilizing effects of impulse in delayed BAM neural networks. Modern Phys Lett B 23(29):3503–3513

    Article  MATH  Google Scholar 

  12. Li CD, Hu WF, Wu SC (2011) Stochastic stability of impulsive BAM neural networks with time delays. Comput Math Appl 61:2313–2316

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang HW, Song QK, Duan CJ (2010) LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions. Math Comput Simul 81:837–850

    Article  MathSciNet  MATH  Google Scholar 

  14. Li HQ, Liao XF, Li CD, Li CJ (2011) Chaos control and synchronization via a novel chatter free sliding mode control strategy. Neurocomputing 74:3212–3222

    Article  Google Scholar 

  15. Li HQ, Liao XF, Huang HY (2011) Synchronization of uncertain chaotic systems based on neural network and sliding mode control. Acta Physica Sinica 60:020512-1–020512-5

    Google Scholar 

  16. Liu C, Li CD, Liao XF (2011) Variable-time impulses in BAM neural networks with delays. Neurocomputing 74:3286–3295

    Google Scholar 

  17. McEliece R, Posner E, Rodemich E, Venkatesh S (1986) The capacity of the Hopfield associative memory. IEEE Trans Inform Theory 33:461–482

    Google Scholar 

  18. Baldi P (1988) Neural networks, orientations of the hypercube, and algebraic threshold functions. IEEE Trans Inform Theory 34:523–530

    Google Scholar 

  19. Artyomov E, Yadid-Pecht O (2005) Modified high-order neural network for invariant pattern recognition. Pattern Recogn Lett 26(6):843–851

    Article  Google Scholar 

  20. Rovithakis GA, Chalkiadakis I, Zervakis ME (2004) High-order neural network structure selection for function approximation applications using genetic algorithms. IEEE Trans Syst Man Cybern Part B Cybern 34(1):150–158

    Article  Google Scholar 

  21. Lee TT, Jeng JT (1998) The Chebyshev-polynomials-based unified model neural networks for function approximation. IEEE Trans Syst Man Cybern Part B Cybern 28(5):925–935

    Google Scholar 

  22. Giles CL, Chen D, Miller CB, Chen HH, Sun GZ, Lee YC (1991) Second-order recurrent neural networks for grammatical inference. In: Proceedings of international joint conference on neural networks, IJCNN91, vol 2, pp 273–281

  23. Liou R, Azimi-Sadjadi MR, Dent R (1991) Detection of dim targets in high cluttered background using high order correlation neural network. In: Proceedings of international joint conference on neural networks, IJCNN91, vol 1, pp 701–706

  24. Cao JD, Liang JL, Lam J (2004) Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199:425–436

    Google Scholar 

  25. Li CJ, Li CD, Liao XF, Huang TW (2011) Impulsive effects on stability of high-order BAM neural networks with time delays. Neurocomputing 74:1541–1550

    Google Scholar 

  26. Li CJ, Li CD, Huang TW (2011) Exponential stability of impulsive high-order hopfield-type neural networks with delays and reaction-diffusion. Int J Comput Math 88:3150–3162

    Article  MathSciNet  MATH  Google Scholar 

  27. Liu XZ, Teo KL (2005) Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. IEEE Trans Neural Netw 16(6):1329–1339

    Article  Google Scholar 

  28. Liu XZ, Wang Q (2008) Impulsive stabilization of high-order hopfield-type neural networks with time-varying delays. IEEE Trans Neural Netw 19(1):71–79

    Article  Google Scholar 

  29. Ho DWC, Liang JL, Lam J (2004) Global exponential stability of impulsive high-order BAM neural networks with time-varying delays. Neural Netw 19:1581–1590

    Article  Google Scholar 

  30. Sanchez EN, Perez JP (1999) Input-to-state stability analysis for dynamic NN. IEEE Trans Circuits Syst 46:1395–1398

    Article  MathSciNet  MATH  Google Scholar 

  31. Boyd S, EI-Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in systems and control theory. SIAM, Philadelphia

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Correspondence to Chaojie Li.

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Lu, D., Li, C. Exponential stability of stochastic high-order BAM neural networks with time delays and impulsive effects. Neural Comput & Applic 23, 1–8 (2013). https://doi.org/10.1007/s00521-012-0861-1

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  • DOI: https://doi.org/10.1007/s00521-012-0861-1

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