Skip to main content
SpringerLink
Log in

Oscillation Analysis for a Recurrent Neural Network Model with Distributed Delays

  • Conference paper
Emerging Intelligent Computing Technology and Applications (ICIC 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 304))

Included in the following conference series:

  • 2306 Accesses

Abstract

In this paper, oscillatory behavior of the solutions for a three-note recurrent neural network model with distributed delays and a strong kernel is investigated. Two simple and practical criteria to guarantee the oscillations of the solutions for the system are derived. Some numerical simulations are given to justify our theoretical analysis result.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Chen, S., Zhang, Q., Wang, C.: Existence and Stability of Equilibria of the Continuous-Time Hopfield Neural Network. J. Comput. Appl. Math. 169, 117–125 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Shen, Y., Yu, H., Jian, J.: Delay-dependent Global Asymptotic Stability for Delayed Cellular Neural Networks. Commun. Nonlinear Sci. Numer. Simulat. 14, 1057–1063 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang, Q., Wei, X., Xu, J.: Delay-dependent Global Stability Condition for Delayed Hopfield Neural Networks. Nonlinear Analysis, RWA 8, 997–1002 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Shen, Y., Wang, J.: An Improved Algebraic Criterion for Global Exponential Stability of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Neural Networks 19, 528–531 (2008)

    Article  Google Scholar 

  5. Cao, J., Wang, L.: Global Exponential Stability And Periodicity of Recurrent Neural Networks with Time Delays. IEEE Trans. Circuits Syst. 52, 920–931 (2005)

    Article  MathSciNet  Google Scholar 

  6. Liu, B., Huang, L.: Existence and Exponential Stability of Almost Periodic Solutions for Hopfield Neural Networks with Delays. Neurocomputing 68, 196–207 (2005)

    Article  Google Scholar 

  7. Liu, Y., You, Z., Cao, L.: On the Almost Periodic Solution of Generalized Hopfield Neural Networks with Time-Varying Delays. Neurocomputing 69, 1760–1767 (2006)

    Article  Google Scholar 

  8. Li, J., Yang, J., Wu, W.: Stability and Periodicity of Discrete Hopfield Neural Networks with Column Arbitrary-Magnitude-Dominant Weight Matrix. Neurocomputing 82, 52–61 (2012)

    Article  Google Scholar 

  9. Liao, X., Wong, K., Wu, Z.: Bifurcation Analysis on A Two-Neuron System with Distributed Delays. Physica D 149, 123–141 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhao, H., Wang, L., Ma, C.: Hopf Bifurcation and Stability Analysis on Discrete-Time Hopfield Neural Network With Delay. Nonlinear Analysis: RWA 9, 103–113 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liao, X., Li, S., Chen, G.: Bifurcation Analysis on A Two-Neuron System with Distributed Delays in The Frequency Domain. Neural Networks 17, 545–561 (2004)

    Article  MATH  Google Scholar 

  12. Hajihosseini, A., Lamooki, G.R.R., Beheshti, B., Maleki, F.: The Hopf Bifurcation Analysis on A Time-Delayed Recurrent Neural Network in the Frequency Domain. Neurocomputing 73, 991–1005 (2010)

    Article  Google Scholar 

  13. Chafee, N.: A Bifurcation Problem for A Functional Differential Equation of Finitely Retarded Type. J. Math. Anal. Appl. 35, 312–348 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gyori, I., Lades, G.: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematical Science, Guangxi Normal University, Guilin, Guangxi, China, 541004

    Chunhua Feng

  2. Department of Mathematics, Jimei University, Xiamen, Fujian, China, 361021

    Zhenkun Huang

Authors
  1. Chunhua Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenkun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Machine Learning and Systems Biology Laboratory, School of Electronics and Information Engineering, Tongji University, Shanghai, China

    De-Shuang Huang

  2. Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Phalguni Gupta

  3. Department of Chemistry, University of Louisville, 2320 South Brook Street, 40292, Louisville, Kentucky, USA

    Xiang Zhang

  4. School of Electrical, Computer & Telecommunications Engineering, The University of Wollongong,, 2522, North Wollongong, NSW, Australia

    Prashan Premaratne

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Feng, C., Huang, Z. (2012). Oscillation Analysis for a Recurrent Neural Network Model with Distributed Delays. In: Huang, DS., Gupta, P., Zhang, X., Premaratne, P. (eds) Emerging Intelligent Computing Technology and Applications. ICIC 2012. Communications in Computer and Information Science, vol 304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31837-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31837-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31836-8

  • Online ISBN: 978-3-642-31837-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation