Skip to main content
SpringerLink
Log in

Convergence Analysis of Discrete Delayed Hopfield Neural Networks

  • Conference paper
Advances in Neural Networks - ISNN 2006 (ISNN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3971))

Included in the following conference series:

  • 59 Accesses

Abstract

The convergence of recurrent neural networks is known to be bases of successful applications of the networks. In this paper, the convergence of discrete delayed Hopfield neural networks is mainly investigated. One new sufficient and necessary condition for the delayed network having no one stable state is given. Also, several new sufficient conditions for the delayed networks converging towards a limit cycle with 2-period and with 4-period are respectively obtained. All results established here partly extend the previous results on the convergence of both discrete Hopfield neural networks and discrete delayed Hopfield neural networks in parallel updating mode.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hopfield, J.J.: Neural Networks and Physical Systems Emergent Collective Computational Abilities. Proc. Nat. Acad. Sci. USA 79, 2554–2558 (1982)

    Article  MathSciNet  Google Scholar 

  2. Bruck, J.: On the Convergence Properties of the Hopfield Model. Proceedings IEEE 78, 1579–1585 (1990)

    Article  Google Scholar 

  3. Xu, Z., Kwong, C.P.: Global Convergence and Asymptotic Stability of Asymmetrical Hopfield Neural Networks. J. Mathematical Analysis and Applications 191, 405–426 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lee, D.: New Stability Conditions for Hopfield Neural Networks in Partial Simultaneous Update Mode. IEEE, Trans. Neural Networks 10, 975–978 (1999)

    Article  Google Scholar 

  5. Goles, E.: Antisymmetrical Neural Networks. Discrete Applied Mathematics 13, 97–100 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ma, R., Zhang, Q., Xu, J.: Convergence of Discrete-time Cellular Neural Networks. Chinese J. Electronics 11, 352–356 (2002)

    Google Scholar 

  7. Ma, R., Xi, Y., Gao, H.: Stability of Discrete Hopfield Neural Networks with Delay in Serial Mode. In: Yin, F.-L., Wang, J., Guo, C. (eds.) ISNN 2004. LNCS, vol. 3173, pp. 126–131. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Qiu, S., Tang, E.C.C., Yeung, D.S.: Stability of Discrete Hopfield Neural Networks with Time-delay. In: Proceedings of IEEE International Conference on System, Man Cybernetics, pp. 2546–2552 (2000)

    Google Scholar 

  9. Ma, R., Xi, Y., Lei, S.: Dynamic Behavior of Discrete Hopfield Neural Networks with Time-Delay. Chinese J. Electronics 14, 187–191 (2005)

    Google Scholar 

  10. Ma, R., Lei, S., Zhang, S.: Dynamic Behavior Analysis of Discrete Neural Networks with Delay. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 259–264. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Highway, Chang’an University, Xi’an, 710064, China

    Sheng-Rui Zhang

  2. University Key Lab of Information Sciences and Engineering, Dalian University, 116622, China

    Sheng-Rui Zhang & Run-Nian Ma

  3. Telecommunication Engineering Institute, Air Force Engineering University, Xi’an, 710077, China

    Run-Nian Ma

Authors
  1. Sheng-Rui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Run-Nian Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  2. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

  3. Department of Electrical Engineering, University of Louisville, 40292, Louisville, KY, U.S.A

    Jacek M. Zurada

  4. Laboratory for Computational Biology, Shanghai Center for Systems Biomedicine, 800 Dong Chuan Rd., 200240, Shanghai, China

    Bao-Liang Lu

  5. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, SR., Ma, RN. (2006). Convergence Analysis of Discrete Delayed Hopfield Neural Networks. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_41

Download citation

  • DOI: https://doi.org/10.1007/11759966_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34439-1

  • Online ISBN: 978-3-540-34440-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation