Skip to main content
SpringerLink
Log in

On the Dynamics in High-Order Cellular Neural Networks with Time-Varying Delays

  • Original Research
  • Published:
Differential Equations and Dynamical Systems Aims and scope Submit manuscript

Abstract

In this paper, the uniform boundedness and exponential stability analysis problems are considered for a class of high-order neural networks with time-varying delays. Without assuming the boundedness on the activation functions, some sufficient conditions are derived for checking the existence, uniqueness and exponential stability of equilibrium point and uniform boundedness for this system by using Brouwer’s fixed point and employing analysis technique. It is believed that these results are significant and useful for the design and applications of HCNNs. Finally, two examples with numerical simulation are given to show the effectiveness of the proposed method and results.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Cao J.D.: New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys. Lett. A 307, 136–147 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cao J.D., Ho D.W.C.: A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach. Chaos Solitons Fractals 24, 1317–1329 (2004)

    Article  MathSciNet  Google Scholar 

  4. Cao J.D., Song Q.K.: Stability in Cohen–Grossberg type BAM neural networks with time-varying delays. Nonlinearity 19(7), 1601–1617 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cao J.D., Wang J.: Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Netw. 17, 379–390 (2004)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen Z., Zhao D.H., Ruan J.: Dynamic analysis of high-order Cohen–Grossberg neural networks with time delay. Chaos Solitons Fractals 32(4), 1538–1546 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dembo A., Farotimi O., Kailath T.: High-order absolutely stable neural networks. IEEE Trans. Circuits Syst. 38, 57–65 (1991)

    Article  MATH  Google Scholar 

  9. Guan Z.H., Sun D.B., Shen J.J.: Qualitative analysis of high-order Hopfield neural networks. Acta Electron. Sin. 28, 77–80 (2000)

    Google Scholar 

  10. Huang L.H., Huang C.X., Liu B.W.: Dynamics of a class of cellular neural networks with time-varying delays. Phys. Lett. A 345, 330–344 (2005)

    Article  MATH  Google Scholar 

  11. Jake H.: Theory of Functional Differential Equations. Springer, New York (2003)

    Google Scholar 

  12. Jiang H.J., Cao J.D.: Global exponential stability of periodic neural networks with time-varying delays. Neurocomputing 70, 343–350 (2006)

    Article  Google Scholar 

  13. Jiang H.J., Teng Z.D.: Global exponential stability of cellular neural networks with time-varying coefficients and delays. Neural Netw. 17, 1415–1425 (2004)

    Article  MATH  Google Scholar 

  14. Jiang H.J., Teng Z.D.: Some new results for recurrent neural networks with varying-time coefficients and delays. Phys. Lett. A 338, 446–460 (2005)

    Article  MATH  Google Scholar 

  15. Jiang H.J., Li Z.M., Teng Z.D.: Boundedness and stability for nonautonomous cellular neural networks with delay. Phys. Lett. A 306, 313–325 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Karayiannis N.B., Venetsanopoulos A.N.: On the training and performance of high-order neural networks. Math. Biosci. 129(2), 143–168 (1995)

    Article  MATH  Google Scholar 

  17. Kosmatopoulos E.B., Christodoulou M.A.: Structural properties of gradient recurrent high-order neural networks. IEEE Trans. Circuits Syst. II 42, 592–603 (1995)

    Article  MATH  Google Scholar 

  18. Kosmatopoulos E.B., Polycarpou M.M., Christodoulou M.A., Ioannou P.A.: High-order neural network structures for identification of dynamical systems. IEEE Trans. Neural Netw. 6, 422–431 (1995)

    Article  Google Scholar 

  19. Liao X.F., Liu Q., Zhang W.: Delay-dependent asymptotic stability for neural networks with distributed delays. Nonlinear Anal. Real World Appl. 7, 1178–1192 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lou X.Y., Cui B.T.: Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays. J. Math. Anal. Appl. 330, 144–158 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Psaltis D., Park C.H., Hong J.: Higher order associative memories and their optical implementations. Neural Netw. 1, 143–163 (1988)

    Article  Google Scholar 

  22. Ren F.L., Cao J.D.: LMI-based criteria for stability of high-order neural networks with time-varying delay. Nonlinear Anal. Real World Appl. 7, 967–979 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ren F., Cao J.: Periodic oscillation of higher-order BAM neural networks with periodic coefficients and delays. Nonlinearity 20(3), 605–629 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang Z.D., Fang J.A., Liu X.H.: Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos Solitons Fractals 36, 388–396 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. Xiang H., Yan K.M., Wang B.Y.: Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks. Phys. Lett. A 352, 341–349 (2006)

    Article  MATH  Google Scholar 

  26. Xu B.J., Liu X.Z., Liao X.X.: Global asymptotic Stability of high-order Hopfield type neural networks with time delays. Comput. Math. Appl. 45, 1729–1737 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  27. Xu B.J., Liu X.Z., Liao X.X.: Global exponential stability of high order Hopfield type neural networks. Appl. Math. Comput. 174, 98–116 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhao H.Y., Mao Z.S.: Dynamics of Cohen–Grossberg neural networks with variable and distributed delays. Physica D 234, 11–22 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhao H.Y., Wang G.L.: Delay-independent exponential stability of recurrent neural networks. Phys. Lett. A 333, 399–407 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics Science, Xinjiang Normal University, Urumqi, 830054, People’s Republic of China

    Haibo Gu

  2. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Haijun Jiang & Zhidong Teng

Authors
  1. Haibo Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haijun Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhidong Teng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haijun Jiang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gu, H., Jiang, H. & Teng, Z. On the Dynamics in High-Order Cellular Neural Networks with Time-Varying Delays. Differ Equ Dyn Syst 19, 119–132 (2011). https://doi.org/10.1007/s12591-010-0044-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12591-010-0044-4

Keywords

Search

Navigation