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Dynamic analysis of discrete-time BAM neural networks with stochastic perturbations and impulses

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Abstract

This paper addresses the problem of stability analysis for a class of uncertain discrete-time stochastic BAM neural networks with time-varying delays and impulses. In this paper, we assume that stochastic disturbances are described by the Brownian motion and jumping parameters are generated from discrete-time discrete-state homogeneous Markov process. By employing the Lyapunov–Krasovskii functional and stochastic analysis theory, a set of novel sufficient conditions are derived to guarantee the robust global exponential stability of the equilibrium point in the mean square. The obtained results are shown to be less conservative than the existing one in the literature. Note that the obtained results are formulated in terms of linear matrix inequality (LMI) that can efficiently solved by the LMI toolbox in Matlab. Numerical examples are given to show that the proposed result significantly improve the allowable upper bounds of delays over some existing results in the literature.

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References

  1. Arik S (2006) Global asymptotic stability of hybrid BAM neural networks with time delays. Phys Lett A 351:85–91

    Article  MATH  Google Scholar 

  2. Barakat M, Lefebvre D, Khalil M, Druaux F, Mustapha O (2013) Parameter selection algorithm with self adaptive growing neural network classifier for diagnosis issues. Int J Mach Learn Cybern 4(3): 217–233

    Article  Google Scholar 

  3. Cao J, Ho DWC, Huang X (2007) LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay. Nonlinear Anal 66:1558–1572

    Article  MATH  MathSciNet  Google Scholar 

  4. Cao J (2003) Global asymptotic stability of delayed bi-directional associative memory neural networks. Appl Math Comput 142:333–339

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen A, Huang L, Cao J (2003) Existence and stability of almost periodic solution for BAM neural networks with delays. Appl Math Comput 137:177–193

    Article  MATH  MathSciNet  Google Scholar 

  6. Gao M, Cui BT (2009) Global robust exponential stability of discrete-time interval BAM neural networks with time-varying delays. Appl Math Model 33:1270–1284

    Article  MATH  MathSciNet  Google Scholar 

  7. Gan Q (2013) Synchronization of competitive neural networks with different time scales and time-varying delay based on delay partitioning approach. Int J Mach Learn Cybern 4(4):327–337

    Article  Google Scholar 

  8. Huang X, Cao J, Huang DS (2005) LMI-Based approach for delay-dependent exponential stability analysis of BAM neural networks. Chaos Solitons Fractals 24:885–898

    Article  MATH  MathSciNet  Google Scholar 

  9. Ho DWC, Liang JL, Lam J (2006) Global exponential stability of impulsive high-order BAM neural networks with time-varying delays. Neural Netw 19:1581–1590

    Article  MATH  Google Scholar 

  10. Kosko B (1987) Adaptive bidirectional associative memories. Appl Opt 26:4947–4960

    Article  Google Scholar 

  11. Kosko B (1988) Bi-directional associative memories. IEEE Trans Syst Man Cybernet 18:49–60

    Article  MathSciNet  Google Scholar 

  12. Liang JL, Cao JD (2004) Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays. Chaos Solitons Fractals 22:773–785

    Article  MATH  MathSciNet  Google Scholar 

  13. Li K, Zhang L, Zhang X, Li Z (2010) Stability in impulsive Cohen–Grossberg-type BAM neural networks with distributed delays. Appl Math Comput 215:3970–3984

    Article  MATH  MathSciNet  Google Scholar 

  14. Liu Y, Wang Z, Liu X (2007) Robust stability of discrete-time stochastic neural networks with time-varying delays. Neurocomputing 71:823–833

    Article  Google Scholar 

  15. Liu Y, Wang Z, Liang J, Liu X (2008) Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans Syst Man Cybern Part B 38:1314–1325

    Article  Google Scholar 

  16. Liu X, Tang M, Martin R, Liu X (2007) Discrete-time BAM neural networks with variable delays. Phys Lett A 367:322–330

    Article  MATH  Google Scholar 

  17. Lou X, Cui B (2006) On the global robust asymptotic stability of BAM neural networks with time-varying delays. Neurocomputing 70:273–279

    Article  Google Scholar 

  18. Liang J, Wang Z, Liu Y, Liu X (2008) Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances. IEEE Trans Syst Man Cybern Part B 38:1073–1083

    Article  Google Scholar 

  19. Liang J, Wang Z, Liu X (2008) Exponential synchronization of stochastic delayed discrete-time complex networks. Nonlinear Dyn 53:153–165

    Article  MATH  MathSciNet  Google Scholar 

  20. Mohamad S (2001) Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks. Physica D 159:233–251

    Article  MATH  MathSciNet  Google Scholar 

  21. Park JH, Kwon OM (2008) On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time- varying delays. Appl Math Comput 199(2):435–446

    Article  MATH  MathSciNet  Google Scholar 

  22. Park JH (2006) Robust stability of bidirectional associative memory neural networks with time delays. Phys Lett A 349:494–499

    Article  Google Scholar 

  23. Raja R, Marshal Anthoni S (2011) Global exponential stability of BAM neural networks with time-varying delays: the discrete-time case. Commun Nonlinear Sci Numer Simul 16:613–622

    Article  MATH  MathSciNet  Google Scholar 

  24. Samidurai R, Sakthivel R, Anthoni SM (2009) Global asymptotic stability of BAM neural networks with mixed delays and impulses. Appl Math Comput 212:113–119

    Article  MATH  MathSciNet  Google Scholar 

  25. Sakthivel R, Samidurai R, Marshal Anthoni S (2010) Exponential stability for stochastic neural networks of neutral type with impulsive effetcs. Modern Phys Lett B 24:1099–1110

    Article  MATH  MathSciNet  Google Scholar 

  26. Sakthivel R, Samidurai R, Marshal Anthoni S (2010) Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects. J Optim Theory Appl 147(3):583–596

    Article  MATH  MathSciNet  Google Scholar 

  27. Sakthivel R, Samidurai R, Marshal Anthoni S (2010) New exponential stability criteria for stochastic BAM neural networks with impulses. Physica Scripta 82:045802

    Article  Google Scholar 

  28. Song Q, Cao JD (2007) Dynamics of bidirectional associative memory networks with distributed delays and reaction-diffusion terms. Nonlinear Anal Real World Appl 8:345–361

    Article  MATH  MathSciNet  Google Scholar 

  29. Sarlin P (2012) Visual tracking of the millennium development goals with a fuzzified self-organizing neural network. Int J Mach Learn Cybern 3(3):233–245

    Article  Google Scholar 

  30. Song Q, Wang Z (2007) A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays. Phys Lett A 368:134–145

    Article  Google Scholar 

  31. Zhang BY, Xu SY, Zou Y (2008) Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays Neurocomputing 72:321–330

    Article  Google Scholar 

  32. Zhao H (2002) Global stability of bidirectional associative memory neural networks with distributed delays. Phys Lett A 297:182–190

    Article  MATH  MathSciNet  Google Scholar 

  33. Zhou Q (2009) Global exponential stability of BAM neural networks with distributed delays and impulses. Nonlinear Anal Real World Appl 10:144–153

    Article  MATH  MathSciNet  Google Scholar 

  34. Zhou Q, Wan L (2009) Impulsive effects on stability of Cohen–Grossberg-type bidirectional associative memory neural networks with delays. Nonlinear Anal Real World Appl 10:25–31

    MathSciNet  Google Scholar 

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Acknowledgments

The authors are very much thankful to the reviewers and editors for their valuable comments and suggestions for improving this work. The work of the corresponding author was supported by “UGC-BSR Start-Up Grant”.

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Authors and Affiliations

  1. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004, India

    R. Raja

  2. Department of Mathematics, Anna University Regional Centre, Coimbatore, 641 047, India

    U. Karthik Raja & A. Leelamani

  3. Department of Mathematics, Thiruvalluvar University, Vellore, 632 115, India

    R. Samidurai

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  1. R. Raja
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  2. U. Karthik Raja
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  3. R. Samidurai
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  4. A. Leelamani
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Correspondence to R. Raja.

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Raja, R., Raja, U.K., Samidurai, R. et al. Dynamic analysis of discrete-time BAM neural networks with stochastic perturbations and impulses. Int. J. Mach. Learn. & Cyber. 5, 39–50 (2014). https://doi.org/10.1007/s13042-013-0199-8

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  • DOI: https://doi.org/10.1007/s13042-013-0199-8

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