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International Symposium on Neural Networks

ISNN 2005: Advances in Neural Networks – ISNN 2005 pp 132–141Cite as

Global Exponential Stability of Recurrent Neural Networks with Infinite Time-Varying Delays and Reaction-Diffusion Terms

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

Abstract

The global exponential stability is discussed for a general class of recurrent neural networks with infinite time-varying delays and reaction-diffusion terms. Several new sufficient conditions are obtained to ensure global exponential stability of the equilibrium point of recurrent neural networks with infinite time-varying delays and reaction-diffusion terms. The results extend the earlier publications. In addition, an example is given to show the effectiveness of the obtained results.

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References

  1. Lu, H.T., Chung, F.L., He, Z.Y.: Some Sufficient Conditions for Global Exponential Stability of Hopfield Neural Networks. Neural Networks 17, 537–544 (2004)

    Article  MATH  Google Scholar 

  2. Civalleri, P.P., Gilli, L.M., Pabdolfi, L.: On Stability of Cellular Neural Networks with Delay. IEEE Transactions on Circuits and Systems 40, 157–164 (1993)

    Article  MATH  Google Scholar 

  3. Baldi, P., Atiga, A.F.: How Delays Affect Neural Dynamics and Learning. IEEE Transactions on Neural Networks 5, 612–621 (1994)

    Article  Google Scholar 

  4. Chen, T.P.: Global Exponential Stability of Delayed Hopfield Neural Networks. Neural Networks 14, 977–980 (2001)

    Article  Google Scholar 

  5. Cao, J.D., Wang, J.: Global Asymptotic Stability of a General Class of Recurrent Neural Networks with Time-varying Delays. IEEE Transactions on Circuits and Systems I 50, 34–44 (2003)

    Article  MathSciNet  Google Scholar 

  6. Cao, J.D., Wang, L.: Exponential Stability and Periodic Oscillatory Solution in BAM Networks with Delays. IEEE Transactions on Neural Networks 13, 457–463 (2002)

    Article  Google Scholar 

  7. Cao, J.D.: Global Stability Conditions for Delayed CNNs. IEEE Transactions on Circuits and Systems-I 48, 1330–1333 (2001)

    Article  MATH  Google Scholar 

  8. Cao, J.D.: A Set of Stability Criteria for Delayed Cellular Neural Networks. IEEE Transactions on Circuits and Systems-I 48, 494–498 (2001)

    Article  MATH  Google Scholar 

  9. Chen, T.P., Rong, L.B.: Delay-independent Stability Analysis of Cohen-Grossberg Neural Networks. Physics Letters A 317, 436–449 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Cao, J.D.: An Estimation of the Domain of Attraction and Convergence Rate for Hopfield Continuous Feedback Neural Networks. Physics Letters A 325, 370–374 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhang, J.Y.: Global Exponential Satbility of Neural Networks with Varible Delays. IEEE Transactions on Circuits and Systems I 50, 288–291 (2003)

    Article  Google Scholar 

  12. Liao, X., Chen, G., Sanches, E.: Delay-dependent Exponentional Stability Analysis of Delayed Neural Networks: an LMI approach. Neural Networks 15, 855–866 (2002)

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Cao, J.D., Ho, D.W.C.: A General Framework for Global Asymptotic Stability Analysis of Delayed Neural Networks Based on LMI approach. Chaos, Solitons & Fractals 24, 1317–1329 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhao, H.Y.: Global Asymptotic Stability of Hopfield Neural Network Involving Distributed Delays. Neural Networks 17, 47–53 (2004)

    Article  MATH  Google Scholar 

  16. Arik, S.: Global Asymptotic Stability of a Large Class of Neural Networks with Constant Time Delay. Physics Letters A 311, 504–511 (2003)

    Article  MATH  Google Scholar 

  17. Sun, C.Y., Feng, C.B.: Global Robust Exponential Stability of Interval Neural Networks with Delays. Neural Process Letters 17, 107–115 (2003)

    Article  Google Scholar 

  18. Sun, C.Y., Feng, C.B.: Exponential Periodicity and Stability of Delayed Neural Networks. Mathematics and Computers in Simulation 66, 469–478 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Cao, J.D., Huang, D.S., Qu, Y.Z.: Global Robust Stability of Delayed Recurrent Neural Networks. Chaos, Solitons & Fractals 23, 221–229 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. Cao, J.D., Liang, J.L., Lam, J.: Exponential Stability of High-order Bidirectional Associative Memory Neural Networks with Time Delays. Physica D: Nonlinear Phenomena 199, 425–436 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  21. Cao, J.D., Liang, J.L.: Boundedness 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 

  22. Cao, J.D., Wang, J.: Absolute Exponential Stability of Recurrent Neural Networks with Time Delays and Lipschitz-continuous Activation Functions. Neural Networks 17, 379–390 (2004)

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  24. Zeng, Z.G., Fu, C.J., Liao, X.X.: Stability Analysis of Neural Networks with Infinite Time-varying Delay. Journal of Mathematics 22, 391–396 (2002)

    MathSciNet  Google Scholar 

  25. Liao, X.X., Fu, Y.L., Gao, J., Zhao, X.Q.: Stability of Hopfield Neural Networks with Reaction-diffusion Terms. Acta Electronica Sinica 28, 78–80 (2000) (in chinese)

    Google Scholar 

  26. Wang, L.S., Xu, D.Y.: Global Exponential Stability of Hopfield Reaction-diffusion Neural Networks with Time-varying Delays. Sci. China Ser. F 46, 466–474 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  27. Liao, X.X., Li, J.: Stability in Gilpin-Ayala Competition Models with Diffusion. Nonliear Analysis 28, 1751–1758 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  28. Liang, J.L., Cao, J.D.: Global Exponential Stability of Reaction-diffusion Recurrent Neural Networks with Time-varying Delays. Physics Letters A 314, 434–442 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  29. Song, Q.K., Zhao, Z.J., Li, Y.M.: Global Exponential Stability of BAM Neural Networks with Distributed Delay and Reaction-diffusion Terms. Physics Letters A 335, 213–225 (2005)

    Article  MATH  Google Scholar 

  30. Song, Q.K., Cao, J.D.: Global Exponential Stability and Existence of Periodic Solutions in BAM Networks with Delays and Reaction-diffusion Terms. Chaos, Solitons & Fractals 23, 421–430 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Huzhou University, Huzhou, Zhejiang, 313000, China

    Qiankun Song, Zhenjiang Zhao & Xuedong Chen

  2. Department of Computation Science, Chengdu University of Information Technology, Chengdu, 610041, China

    Qiankun Song

Authors
  1. Qiankun Song
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  2. Zhenjiang Zhao
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  3. Xuedong Chen
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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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Cite this paper

Song, Q., Zhao, Z., Chen, X. (2005). Global Exponential Stability of Recurrent Neural Networks with Infinite Time-Varying Delays and Reaction-Diffusion Terms. 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_20

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  • DOI: https://doi.org/10.1007/11427391_20

  • 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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