Advertisement

Journal of Systems Science and Complexity

, Volume 31, Issue 3, pp 608–620 | Cite as

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions of a General Delayed BAM Neural Networks

  • Lian Duan
Article

Abstract

This paper studies a class of general BAM neural networks with multiple delays. Employing the exponential dichotomy theory and fixed point method, together with constructing suitable Lyapunov functionals, easily verifiable delay-independent criteria are established to ensure the existence and global exponential stability of pseudo almost periodic solutions, which not only generalize but also complement some existing ones. These theoretical results are also supported with numerical simulations.

Keywords

General BAM neural network global exponential stability pseudo almost periodic solution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The author would like to express the sincere appreciation to the editor and reviewer for their helpful comments in improving the presentation and quality of the paper. In particular, the author expresses the sincere gratitude to Prof. LI Dequan for the helpful discussion when this revision work was being carried out.

References

  1. [1]
    Kosko B, Adaptive bi-directional associative memories, Appl. Opt., 1987, 26: 4947–4960.CrossRefGoogle Scholar
  2. [2]
    Kosko B, Bi-directional associative memories, IEEE Trans. Systems Man Cybernet., 1988, 18: 49–60.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Cao J and Wang L, Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Trans. Neural Netw., 2002, 13: 457–463.CrossRefGoogle Scholar
  4. [4]
    Chen A, Huang L, and Cao J, Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput., 2003, 137: 177–193.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Ho Daniel W, Liang J, and Lam J, Global exponential stability of impulsive high-order BAM neural networks with time-varying delays, Neural Netw., 2006, 19: 1581–1590.CrossRefzbMATHGoogle Scholar
  6. [6]
    Song Q, Zhao Z, and Li Y, Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms, Phys. Lett. A, 2005, 235: 213–225.CrossRefzbMATHGoogle Scholar
  7. [7]
    Duan L, Huang L, and Guo Z, Global robust dissipativity of interval recurrent neural networks with time-varying delay and discontinuous activations, Chaos, 2016, 26: 073101.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Park J, A novel criterion for global asymptotic stability of BAM neural networks with time delays, Chaos Solitons Fractals, 2006, 29: 446–453.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Zhang L and Si L, Existence and exponential stability of almost periodic solution for BAM neural networks with variable coefficients and delays, Appl. Math. Comput., 2007, 194: 215–223.MathSciNetzbMATHGoogle Scholar
  10. [10]
    Duan L and Huang L, Global exponential stability of fuzzy BAM neural networks with distributed delays and time-varying delays in the leakage terms, Neural Comput. Appl., 2013, 23: 171–178.CrossRefGoogle Scholar
  11. [11]
    Ding K and Huang N, Global robust exponential stability of interval general BAM neural network with delays, Neural Process. Lett., 2006, 23: 171–182.CrossRefGoogle Scholar
  12. [12]
    Zhang Z and Zhou D, Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks, J. Franklin Inst., 2010, 347: 763–780.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Zhang Z and Liu K, Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales, Neural Netw., 2011, 24: 427–439.CrossRefzbMATHGoogle Scholar
  14. [14]
    Zhang Z, Yang Y, and Huang Y, Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays, Neural Netw., 2011, 24: 457–465.CrossRefzbMATHGoogle Scholar
  15. [15]
    Ammar B, Chérif F, and Alimi A, Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays, IEEE Trans. Neural Netw., 2012, 23: 109–117.CrossRefGoogle Scholar
  16. [16]
    Ait Dads E and Ezzinbi K, Pseudo almost periodic solutions of some delay differential equations, J. Math. Anal. Appl., 1996, 201: 840–850.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Fink A M, Almost Periodic Differential Equations, Lecture Notes in Mathematics, Springer-Verlag, New York, 1974.CrossRefGoogle Scholar
  18. [18]
    Zhang C, Almost Periodic Type Functions and Ergodicity, Kluwer Academic/Science Press, Beijing, 2003.CrossRefzbMATHGoogle Scholar
  19. [19]
    Zhang C, Pseudo almost periodic solutions of some differential equations II, J. Math. Anal. Appl., 1995, 192: 543–561.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Qin S, Xue X, and Wang P, Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations, Inform. Sci., 2013, 220: 367–378.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Lu W and Chen T, Almost periodic dynamics of a class of delayed neural networks with discontinuous activations, Neural Comput., 2008, 20: 1065–1090.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    Duan L, Huang L, and Guo Z, Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations, Nonlinear Dyn., 2014, 77: 1469–1484.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematics and Big DataAnhui University of Science and TechnologyHuainanChina

Personalised recommendations