Skip to main content
Springer Nature Link
Log in

Exponential Stability of Neural Networks with Distributed Time Delays and Strongly Nonlinear Activation Functions

  • Conference paper
Save conference paper
View saved research
Neural Information Processing (ICONIP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4232))

Included in the following conference series:

  • 1563 Accesses

Abstract

In this paper, we provided a new technique based on the concept of comparison. Different from the Lyapunov method, the new technique showed that if the given conditions hold then the any state of neural networks with distributed time delays and strongly nonlinear activation functions is always bounded by exponential convergence function. In addition, some sufficient conditions are obtained to guarantee that such neural network is globally exponentially stable, or locally exponentially stable. Furthermore, we obtained the estimates of the exponential convergence rates and the region of exponential convergence.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

References

  1. Forti, M., Tesi, A.: New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circ. Syst. I 42, 354–366 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chen, T.P., Rong, L.B.: Robust Global Exponential Stability of Cohen- Grossberg Neural Networks with Time-Delays. IEEE Transactions on Neural Networks 15, 203–206 (2004)

    Article  Google Scholar 

  3. Liao, X.F., Li, C.G., Wong, K.W.: Criteria for Exponential Stability of Cohen- Grossberg Neural Networks. Neural Networks 17, 1401–1414 (2004)

    Article  MATH  Google Scholar 

  4. Xu, D., Yang, Z.: Impulsive Delay Differential Inequality and Stability of Neural Networks. J. Math. Anal. Appl. 305, 107–120 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Liao, X.X., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks with Multiple Time Delays. IEEE Trans. Circ. Syst. I 50, 268–275 (2003)

    Article  MathSciNet  Google Scholar 

  6. Yi, Z., Heng, A., Leung, K.S.: Convergence Analysis of Cellular Neural Networks with Unbounded Delay. IEEE Trans. Circ. Syst. I 48, 680–687 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Zeng, Z.G., Wang, J.: Complete Stability of Cellular Neural Networks with Timevarying Delays. IEEE Trans. on Circuits and Systems-I: Regular Papers 53, 944–955 (2006)

    Article  MathSciNet  Google Scholar 

  8. Cao, J.: Results Concerning Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks. Physics Letters A 307, 136–147 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Zhou, J., Liu, Z., Chen, G.R.: Dynamics of Delayed Periodic Neural Networks. Neural Networks 17, 87–101 (2004)

    Article  MATH  Google Scholar 

  10. Zeng, Z.G., Wang, J.: Multiperiodicity and Exponential Attractivity Evoked by Periodic External Inputs in Delayed Cellular Neural Networks. Neural Computation 18, 848–870 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Arik, S.: An Analysis of Global Asymptotic Stability of Delayed Cellular Neural Networks. IEEE Trans. Neural Networks 13, 1239–1242 (2002)

    Article  Google Scholar 

  12. Liao, T.L., Wang, F.C.: Global Stability for Cellular Neural Networks with Time Delay. IEEE Trans. Neural Networks 11, 1481–1484 (2000)

    Article  Google Scholar 

  13. Zeng, Z.G., Wang, J., Liao, X.X.: Stability Analysis of Delayed Cellular Neural Networks Described Using Cloning Templates. IEEE Trans. Circuits and Syst. I 51, 2313–2324 (2004)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hubei Normal University, Huangshi, Hubei, 435002, China

    Chaojin Fu

  2. Hubei Province Key Laboratory of Bioanalytical Technique, Hubei Normal University, Huangshi, Hubei, 435002, China

    Chaojin Fu

  3. Department of Electric Engineering, ZhongYuan Institute of Technology, Zhengzhou, Henan, 450007, China

    Zhongsheng Wang

Authors
  1. Chaojin Fu
    View author publications

    Search author on:PubMed Google Scholar

  2. Zhongsheng Wang
    View author publications

    Search author on:PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, The Chinese Univ. of Hong Kong, Shatin, N.T., Hong Kong

    Irwin King

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

    Jun Wang

  3. The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Lai-Wan Chan

  4. Department of Computer Science and Engineering & Center for Cognitive Science, The Ohio State University, OH 43210, Columbus

    DeLiang Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fu, C., Wang, Z. (2006). Exponential Stability of Neural Networks with Distributed Time Delays and Strongly Nonlinear Activation Functions. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893028_66

Download citation

Publish with us

Policies and ethics