Advertisement

Asymptotic Stability of Second-Order Discrete-Time Hopfield Neural Networks with Variable Delays

  • Wei Zhu
  • Daoyi Xu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)

Abstract

This paper studies the problem of asymptotic stability of second-order discrete-time Hopfield neural networks with variable delays. By utilizing inequality techniques, we obtain sufficient conditions for the existence and asymptotic stability of an equilibrium point and estimate the region of existence and the attraction domain of the equilibrium point. A numerical example is given to illustrate our theoretical results.

Keywords

Neural Network Equilibrium Point Asymptotic Stability Exponential Stability Attraction Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Xu, D.Y., Zhao, H.Y., Zhu, H.: Global Dynamics of Hopfield Neural Networks Involving Variable Delays. Computers and Mathematics with Applications 42(1-2), 39–45 (2001)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Liao, X.F., Wong, K.W.: Global Exponential Stability for A Class of Retarded Functional Differential Equations with Applications in Neural Networks. J. Math. Anal. Appl. 293(1), 125–148 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Guo, S.J., Huang, L.H., Wang, L.: Exponential Stability of Discrete Hopfield Neural Networks. Computers and Mathematics with Applications 47(8-9), 1249–1256 (2004)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Dembo, A., Farotimi, O., Kailath, T.: High-order Absolutely Stable Neural Networks. IEEE Trans. Circ. Syst. II 38(1), 57–65 (1991)MATHCrossRefGoogle Scholar
  5. 5.
    Xu, B.J., Liu, X.Z., Liao, X.X.: Global Asymptotic Stability of High-Order Hopfield Type Neural Networks with Time Delays. Computers and Mathematics with Applications 45(10-11), 1729–1737 (2003)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Zhang, Y.: Robust Stabilization of Bilinear Uncertain Delay Systems. Journal of UEST of China 22(4), 414–419 (1993) (In Chinese)Google Scholar
  7. 7.
    Cao, J., Liang, J., Lam, J.: Exponential Stability of High-order Bidirectional Associative Memory Neural Networks with Time Delays. Physica D 199(3-4), 425–436 (2004)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Cao, J.: Global Exponential Stability of Hopfield Neural Networks. Int. J. Syst. Sci. 32(2), 233–236 (2001)MATHCrossRefGoogle Scholar
  9. 9.
    Mohamad, S., Gopalsamy, K.: Exponential Stability of Continuous-time and Discrete-time Cellular Neural Networks with Delays. Applied Mathematics and Computation 135(1), 17–38 (2003)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Mohamad, S., Gopalsamy, K.: Dynamics of A Class of Discrete-time Neural Networks and Their Continuous-time Counterparts. Mathematics and Computers in Simulation 53(1-2), 1–39 (2000)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wei Zhu
    • 1
    • 2
  • Daoyi Xu
    • 2
  1. 1.Institute of Applied MathematicsChongqing University of Posts and TelecommunicationsChongqingChina
  2. 2.Institute of MathematicsSichuan UniversityChengduChina

Personalised recommendations