Skip to main content
Log in

Asymptotic behavior of equilibriums of a class of impulsive bidirectional associative memory neural networks with time-varying delays

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, we study the global asymptotic behavior for an impulsive bidirectional associative memory neural network with time-varying delays. The impulses are realized at fixed moments of time. The main stability criteria are proved by employing Lyapunov functions and the Razumikhin technique. An illustrative example is given to demonstrate the effectiveness of the obtained results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Akca H, Alassar R, Covachev V, Covacheva Z, Al-Zahrani E (2004) Continuous-time additive Hopfield-type neural networks with impulses. J Math Anal Appl 290:436–451

    Article  MathSciNet  MATH  Google Scholar 

  2. Ahmad S, Stamova IM (2008) Global exponential stability for impulsive cellular neural networks with time-varying delays. Nonlinear Anal 69:786–795

    Article  MathSciNet  MATH  Google Scholar 

  3. Arbib MA (1987) Brains, machines, and mathematics. Springer, New York

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Cao JD, Dong M (2003) Exponential stability of delayed bi-directional associative memory neural networks. Appl Math Comput 135:105–112

    Article  MathSciNet  MATH  Google Scholar 

  6. Cao JD, Yang Y (2001) Global stability analysis of bi-directional associative memory neural networks with time delay. Int J Circ Theor Appl 29:185–196

    Article  Google Scholar 

  7. Chen AP, Cao JD, Huang LH (2004) Exponential stability of BAM neural networks with transmission delays. Neurocomputing 57:435–454

    Article  Google Scholar 

  8. Gopalsamy K, He X (1994) Delay-independent stability in bi-directional associative memory networks. IEEE Trans Neural Netw 5:998–1002

    Article  Google Scholar 

  9. Haykin S (1998) Neural networks: a comprehensive foundation. Prentice-Hall, Ehglewood Cliffs, NJ

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  12. Kosko B (1992) Neural networks and fuzzy systems—a dynamical system approach machine intelligence. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  13. Lakshmikantham V, Bainov DD, Simeonov PS (1989) Theory of impulsive differential equations. World Scientific, Singapore

    MATH  Google Scholar 

  14. Li Y (2005) Global exponential stability of BAM neural networks with delays and impulses. Chaos Solut Fract 24:279–285

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Rao VSH, Phaneendra BRM (1999) Global dynamics of bi-directional associative memory neural networks involving transmission delays and dead zones. Neural Netw 12:455–465

    Article  Google Scholar 

  17. Song QK, Cao JD (2005) Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms. Chaos Solut Fract 23:421–430

    Article  MathSciNet  MATH  Google Scholar 

  18. Razumikhin BS (1988) Stability of systems with retardation. Nauka, Moscow, (in Russian)

  19. Stamov GT (2008) Existence of almost periodic solutions for impulsive cellular neural networks. RMJM 4:1271–1285

    MathSciNet  Google Scholar 

  20. Stamov GT, Stamova IM (2007) Almost periodic solutions for impulsive neural networks with delay. Appl Math Model 31:1263–1270

    Article  MATH  Google Scholar 

  21. Stamova IM, Stamov GT (2001) Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics. J Comp Appl Math 130:163–171

    Article  MathSciNet  MATH  Google Scholar 

  22. Yan J, Shen J (1999) Impulsive stabilization of impulsive functional differential equations by Lyapunov-Razumikhin functions. Nonlinear Anal 37:245–255

    Article  MathSciNet  MATH  Google Scholar 

  23. Yang Z, Xu D (2005) Stability analysis of delay neural networks with impulsive effects. IEEE Trans Circuit Syst II 52:517–521

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhou Q, Wan L (2009) Impulsive effects on stability of Cohen-Grossberg-type bidirectional associative memory neural networks with delays. Nonlinear Anal RWA 10:2531–2540

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ivanka M. Stamova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stamova, I.M., Ilarionov, R. & Krustev, K. Asymptotic behavior of equilibriums of a class of impulsive bidirectional associative memory neural networks with time-varying delays. Neural Comput & Applic 20, 1111–1116 (2011). https://doi.org/10.1007/s00521-010-0516-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-010-0516-z

Keywords

Navigation