SpringerLink
Log in

Global exponential stability of Hopfield neural networks with variable delays and impulsive effects

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Marcus C M, Westervelt R M. Stability of analog neural networks with delay[J]. Phys Rev A, 1989, 39(1):347–359.

    Article  MathSciNet  Google Scholar 

  2. Panas A I, Yang T, Chua L O. Experimental results of impulsive synchronization between two chua’s circuits[J]. Int J Bifurcation and Chaos, 1998, 8(3):639–644.

    Article  MATH  Google Scholar 

  3. Liu Bin, Liu **nzhi, Liao **aoxin. Robust H-stability of Hopfield neural networks with impulsive effects and design of impulsive controllers[J]. Control Theory and Applications, 2003, 19(2):168–172 (in Chinese).

    Google Scholar 

  4. Akca H, Alassar R, Covachev V, Covacheva Z, Al Zahrani E. Continuous-time additive Hopfieldtype neural networks with impulses[J]. J Math Anal Appl, 2004, 290(2):436–451.

    Article  MATH  MathSciNet  Google Scholar 

  5. Yang Zhichun, Xu Daoyi. Stability analysis of delay neural networks with impulsive effects[J]. IEEE Transactions on Circuits and Systems II, 2005, 52(8):517–521.

    Article  Google Scholar 

  6. Guan Zhihong, Chen Guanrong. On delayed impulsive Hopfield neural networks[J]. Neural Networks, 1999, 12(2):273–280.

    Article  Google Scholar 

  7. Driessche P V D, Zou X F. Global attractivity in delayed Hopfield neural networks models[J]. SIAM J Appl Math, 1998, 58(16):1878–1890.

    Article  MATH  MathSciNet  Google Scholar 

  8. Cao **de, Li Jibin. The stability in neural networks with interneuronal transmission delays[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(5):457–462.

    Article  MATH  MathSciNet  Google Scholar 

  9. Mohamad S. Global exponential stability of continuous-time and discrete-time delayed bidirectional neural networks[J]. Phys D, 2001, 159(3):233–251.

    Article  MATH  MathSciNet  Google Scholar 

  10. Xu Daoyi, Zhao Hongyong, Zhu Hong. Global dynamics of Hopfield neural networks involving variable delays[J]. Computers and Mathematics with Applications, 2001, 42(1):39–45.

    Article  MATH  MathSciNet  Google Scholar 

  11. Wang Linshan, Xu Daoyi. Stability for Hopfield neural networks with time delays[J]. Journal of Vibration and Control, 2002, 8(1):13–18.

    Article  MathSciNet  Google Scholar 

  12. Wang Linshan, Xu Daoyi. Stability analysis of Hopfield neural networks with time delays[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(1):65–70.

    Article  MATH  MathSciNet  Google Scholar 

  13. Guo Shangjiang, Huang Lihong. Stability analysis of a delayed Hopfield neural network[J]. Phys Rev E, 2003, 67(6):1–7.

    MATH  Google Scholar 

  14. Liao **aoxin. Mathematical connotation of physical parameters in Hopfield neural networks[J]. Sience in China, E, 2003, 33(2):127–136 (in Chinese).

    Article  Google Scholar 

  15. Lakshmikantham V, Bainov D D, Simeonov P S. Theory of Impulsive Differential Equations[M]. World Scientific, Singapore, 1989.

    Google Scholar 

  16. Liao **aoxin. Theory and Applications of Stability for Dynamical Systems[M]. National Defence Industry Press, Be**g, 2001, 9–14 (in Chinese).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics College, Chongqing Normal University, Chongqing, 400047, P. R. China

    Yang Zhi-chun  (杨志春) (Associate Professor, Doctor)

  2. Yangtze Center of Mathematics, Sichuan University, Chengdu, 610064, P. R. China

    Yang Zhi-chun  (杨志春) (Associate Professor, Doctor) & Xu Dao-yi  (徐道义)

Authors
  1. Yang Zhi-chun  (杨志春)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xu Dao-yi  (徐道义)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Zhi-chun  (杨志春).

Additional information

Communicated by LIU Zeng-rong

Project supported by the National Natural Science Foundation of China (No.10371083)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, Zc., Xu, Dy. Global exponential stability of Hopfield neural networks with variable delays and impulsive effects. Appl Math Mech 27, 1517–1522 (2006). https://doi.org/10.1007/s10483-006-1109-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-1109-1

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation