Skip to main content
SpringerLink
Log in

Stability of Uncertain Reaction-Diffusion Stochastic BAM Neural Networks with Mixed Delays and Markovian Jumping Parameters

  • Conference paper
Mathematical Modelling and Scientific Computation (ICMMSC 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 283))

  • 1738 Accesses

Abstract

In this paper, sufficient conditions are proposed to study robust asymptotic stability of uncertain reaction-diffusion stochastic Bi-directional Associative Memory (BAM) neural network with time-varying delays and Markovian jumping parameters by using suitable Lyapunov-Krasovokii functional, inequality techniques and Linear Matrix Inequality (LMI). A numerical example is given to illustrate the theory.

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. Kosko, B.: Adaptive bi-directional associative memories. Appl. Opt. 26, 4947–4960 (1987)

    Article  Google Scholar 

  2. Kosko, B.: Bi-directional associative memoriees. IEEE Trans. Syst. Man Cybern. 18, 49–60 (1988)

    Article  MathSciNet  Google Scholar 

  3. Kosko, B.: Neural Networks and Fuzzy System - A Dynamical Systems Approach to Machine Intelligence. Prentice-Hall, NJ (1992)

    MATH  Google Scholar 

  4. Cao, J.: Global asymptotic stability of delayed bi-directional associative memory neural networks. Appl. Math. Comput. 142, 333–339 (2003)

    MathSciNet  MATH  Google Scholar 

  5. Balasubramaniam, P., Rakkiyappan, R., Sathy, R.: Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters. Expert Syst. Appl. 38, 121–130 (2011)

    Article  MATH  Google Scholar 

  6. Balasubramaniam, P., Vidhya, C.: Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction diffusion terms. J. Comput. Appl. Math. 234, 3458–3466 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Wang, L.S., Xu, D.Y.: Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays. Science China (Series F) 46, 466–474 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wang, L., Zhang, Z., Wang, Y.: Stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with markovian jumping parameters. Phys. Lett. A 372, 3201–3209 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gu, K.: An integral inequality in the stability problems of time delay system. In: Proceeding of 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 2805–2810 (2000)

    Google Scholar 

  10. Wang, Z., Liu, Y., Fraser, K., Liu, X.: Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354, 288–297 (2006)

    Article  MATH  Google Scholar 

  11. Boyd, S., Ghoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequlities in system and control theory. SIAM, Philadephia (1994)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, VIT University - Chennai Campus, Chennai, 600 048, India

    C. Vidhya

  2. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, 624 302, Tamil Nadu, India

    P. Balasubramaniam

Authors
  1. C. Vidhya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Balasubramaniam
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Gandhigram Rural University, 624302, Gandhigram, Tamil Nadu, India

    P. Balasubramaniam

  2. Department of Mathematics, Gandhigram Rural Institute - Deemed University, 624302, Gandhigram, Tamil Nadu, India

    R. Uthayakumar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vidhya, C., Balasubramaniam, P. (2012). Stability of Uncertain Reaction-Diffusion Stochastic BAM Neural Networks with Mixed Delays and Markovian Jumping Parameters. In: Balasubramaniam, P., Uthayakumar, R. (eds) Mathematical Modelling and Scientific Computation. ICMMSC 2012. Communications in Computer and Information Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28926-2_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28926-2_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28925-5

  • Online ISBN: 978-3-642-28926-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation