Skip to main content

Global Exponential Stability of Non-autonomous Cellular Neural Network Model with Time Varying Delays

  • Conference paper
  • First Online:
Mathematical Analysis and Applications in Modeling (ICMAAM 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 302))

  • 594 Accesses

Abstract

We have considered a general form of non-autonomous cellular neural network with time varying delays in this paper. We have estimated the upper bound of solutions of the system by introducing different parameters and considered some conditions on it. We have derived the conditions of boundedness and global exponential stability of the model which is initially unstable for some parameter values using Young Inequality technique and Dini derivative. Several examples and their computer simulations are given to illustrate the effectiveness of obtained results.

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

Access this chapter

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 EPUB and 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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. Chua, L.O., Yang, L.: Cellular neural networks: theory. IEEE Trans. Circuits Syst. 35, 1257–1272 (1988)

    Article  MathSciNet  Google Scholar 

  2. Chua, L.O., Yang, L.: Cellular neural networks: applications. IEEE Trans. Circuits Syst. 35, 1273–1290 (1988)

    Article  MathSciNet  Google Scholar 

  3. Jiang, H., Teng, Z.: Dynamics of neural networks with variable coefficients and time-varying delays. Neural Netw. 19, 676–683 (2006)

    Article  Google Scholar 

  4. Li, Q., Wang, S., Wu, Y.: Exponential stability of the neural networks with time-varying discrete and distributed delays. In: 2010 Chinese control and decision conference. IEEE (2010)

    Google Scholar 

  5. Cao, J., Yang, J.: Boundedness and stability for Cohen Grossberg neural network with time-varying delays. J. Math. Anal. Appl. 296, 665–685 (2004)

    Article  MathSciNet  Google Scholar 

  6. Cao, J., Wang, J.: Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst.-I 50, 3444 (2003)

    Google Scholar 

  7. Jiang, M., Shen, Y., Liu, M.: Global exponential stability of non-autonomous neural networks with variable delay. In: Advances in neural networks (2005). ISNN 108–113

    Google Scholar 

  8. Baldi, P., Atiya, A.F.: How delays effect Neural Dynamics and Learning. IEEE Trans. Neural Netw. 5(4) (1994)

    Article  Google Scholar 

  9. Das, P., Kundu, A.: Bifurcation and chaos in delayed cellular neural network model. J. Appl. Math. Phys. 2, 219–224 (2014)

    Article  Google Scholar 

  10. Kundu, A., Das, P.: Global stability, bifurcation, and chaos control in a delayed neural network model. In: Advances in artificial neural systems, vol. 2014, Article ID 369230, 8 p. (2014)

    Google Scholar 

  11. Cao,J., Song, Q.: Stability in Cohen Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19, 1601–1617 (2006)

    Article  MathSciNet  Google Scholar 

  12. Jiang, H., Li, Z., Teng, Z.: Boundedness and stability for nonautonomous cellular neural networks with delay. Phys. Lett. A 306, 313325 (2003)

    Article  MathSciNet  Google Scholar 

  13. Zhang, Q., Wei, X., Xu, J.: Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays. Chaos Solitons Fractals (2008) (Elsevier)

    Google Scholar 

  14. Zhou, L., Zhang, Y.: Global exponential stability of cellular neural networks with multi-proportional delays. Int. J. Biomath. 8(6), 1550071 (17 pages) (2015) (World Scientific Publishing Company)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Das .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chowdhury, M., Das, P. (2020). Global Exponential Stability of Non-autonomous Cellular Neural Network Model with Time Varying Delays. In: Roy, P., Cao, X., Li, XZ., Das, P., Deo, S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore. https://doi.org/10.1007/978-981-15-0422-8_17

Download citation

Publish with us

Policies and ethics