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Exponential Stability of Cohen-Grossberg Neural Networks with Delays

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Advances in Neural Networks – ISNN 2005 (ISNN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3496))

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Abstract

The exponential stability characteristics of the Cohen-Grossberg neural networks with discrete delays are studied in this paper, without assuming the symmetry of connection matrix as well as the monotonicity and differentiability of the activation functions and the self-signal functions. By constructing suitable Lyapunov functionals, the delay-independent sufficient conditions for the networks converge exponentially toward the equilibrium associated with the constant input are obtained. It does not doubt that our results are significant and useful for the design and applications of the Cohen-Grossberg neural networks.

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References

  1. Cohen, M.A., Grossberg, S.: Absolute Stability and Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks. IEEE Transactions on Systems, Man and Cybernetics SMC-13, 815–821 (1981)

    MathSciNet  Google Scholar 

  2. Grossberg, S.: Nonlinear Neural Networks: Principles, Mechanisms, and Architectures. Neural Networks 1, 17–61 (1988)

    Article  Google Scholar 

  3. Hopfield, J.J.: Meuronal Networks and Physical Systems with Emergent Collective Computational Abilities. Proceedings of the National Academy of Sciences 79, 2554–2558 (1982)

    Article  MathSciNet  Google Scholar 

  4. Hopofield, J.J.: Neurons with Graded Response Have Collective Computational Properties Like Those of Two-state Neurons. Proceeding of the National Academy of Sciences 81, 3058–3092 (1984)

    Google Scholar 

  5. Vander, D.P., Zou, X.: Global Attractivity in Delayed Hopfield Neural Network Models. SIAM Journal of on Applied Mathematics 58, 1878–1890 (1998)

    Article  Google Scholar 

  6. Marcus, C.M., Westervelt, R.M.: Stability of Analog Neural Networks with Delay. Physical Review A 39, 347–359 (1989)

    Article  MathSciNet  Google Scholar 

  7. Gopalsamy, K., He, X.: Stability in Asymmetric Hopfield Nets with Transmission Delays. Physica D 76, 344–358 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gopalsamy, K., He, X.: Delay-independent Stability in Bi-directional Associative Memory Networks. IEEE Transactions on Neural Networks 5, 998–1002 (1994)

    Article  Google Scholar 

  9. Wang, L., Zou, X.: Harmless Delays in Cohen-Grossberg Neural Networks. Physical D 170, 162–173 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ye, H., Michel, A.N., Wang, K.: Qualitative Analysis of Cohen-Grossberg Neural Networks with Multiple Delays. Physical Review E 51, 2611–2618 (1995)

    Article  MathSciNet  Google Scholar 

  11. Joy, M.: Results Concerning the Absolute Stability of Delayed Neural Networks. Neural Networks 13, 613–616 (2000)

    Article  Google Scholar 

  12. Sree Hari Rao, V., Phaneendra, B.R.M.: Global Dynamics of Bi-directional Associative Memory Neural Networks Involving Transmission Delays and Dead Zones. Neural Networks 12, 455–465 (1999)

    Article  Google Scholar 

  13. Liao, X.F., Yu, J.B.: Robust Stability for Interval Hopfield Neural Networks with Time Delays. IEEE Transactions on Neural Networks 9, 1042–1046 (1998)

    Article  Google Scholar 

  14. Liao, X.F., Wong, K.W., Wu, Z.F., Chen, G.: Novel Robust Stability Criteria for Interval Delayed Hopfield Neural Networks. IEEE Transactions on CAS-I 48, 1355–1359 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Liao, X.F., Yu, J.B.: Qualitative Analysis of Bi-directional Associative Memory Networks with Time Delays. Int. J. Circuit Theory and Applicat. 26, 219–229 (1998)

    Article  MATH  Google Scholar 

  16. Liao, X.F., Yu, J.B., Chen, G.: Novel Stability Criteria for Bi-directional Associative Memory Neural Networks with Time Delays. Int. J. Circuit Theory and Application 30, 519–546 (2002)

    Article  MATH  Google Scholar 

  17. Liao, X.F., Wong, K.W., Yu, J.B.: Novel Stability Conditions for Cellular Neural Networks with Time Delay. Int. J. Bifur. And Chaos 11, 1853–1864 (2002)

    Article  Google Scholar 

  18. Liao, X.F., Wu, Z.F., Yu, J.B.: Stability Analyses for Cellular Neural Networks with Continuous Delay. Journal of Computational and Applied Math. 143, 29–47 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Liao, X.F., Chen, G., Sanchez, E.N.: LMI-based Approach for Asymptotically Stability Analysis of Delayed Neural Networks. IEEE Transactions on CAS-I 49, 1033–1039 (2002)

    Article  MathSciNet  Google Scholar 

  20. Liao, X.F., Chen, G., Sanchez, E.N.: Delay-dependent Exponential Stability Analysis of Delayed Neural Networks: an LMI Npproach. Neural Networks 15, 855–866 (2002)

    Article  Google Scholar 

  21. Gopalsamy, K.: Stability and Oscillations in Delays Differential Equations of Population Dynamics. Kluwer, Dordrecht (1992)

    Google Scholar 

  22. Cao, J., Liang, J.: Boundness and Stability for Cohen-Grossberg Neural Networks with Time-varying Delays. Journal of Mathematical Analysis and Applications 296, 665–685 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Yuan, K., Cao, J.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Multiple Time-varying Delays. In: Yin, F.-L., Wang, J., Guo, C. (eds.) ISNN 2004. LNCS, vol. 3173, pp. 78–83. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  24. 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, 34–44 (2003)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Chongqing University, Chongqing, 400044, China

    Wei Zhang

  2. College of Information, Southwest Agricultural University, 400716, Chongqing, China

    Jianqiao Yu

  3. Department of Computer and Modern Education Technology, Chongqing Education College, Chongqing, 400067, China

    Wei Zhang

Authors
  1. Wei Zhang
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  2. Jianqiao Yu
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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. The Key Laboratory of Optoelectric Technology & Systems, Ministry of Education, China

    Xiaofeng Liao

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

    Zhang Yi

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© 2005 Springer-Verlag Berlin Heidelberg

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Zhang, W., Yu, J. (2005). Exponential Stability of Cohen-Grossberg Neural Networks with Delays. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_22

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  • DOI: https://doi.org/10.1007/11427391_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25912-1

  • Online ISBN: 978-3-540-32065-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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