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Global exponential stability of a class of neural networks with unbounded delays

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Ukrainian Mathematical Journal Aims and scope

In this paper, the global exponential stability of a class of neural networks is investigated. The neural networks contain variable and unbounded delays. By constructing a suitable Lyapunov function and using the technique of matrix analysis, we obtain some new sufficient conditions for global exponential stability.

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References

  1. P. P. Civalleri, L. M. Gilli, and L. Pandolfi, “On stability of cellular neural networks with delay,” IEEE Trans. Circuits Syst.-I, 40, 157–164 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  2. H. Jiang and Z. Teng, “Global exponential stability of cellular neural networks with time-varying coefficients and delay,” Neural Networks, 17, 1415–1425 (2004).

    Article  MATH  Google Scholar 

  3. B. Liu and L. Huang, “Existence and exponential stability of almost periodic solutions for cellular neural networks with continuously distributed delays,” J. Korean Math. Soc., 43, 445–459 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  4. W. Lu, L. Rong, and T. Chen, “Global convergence of delayed neural network systems,” Int. J. Neural Syst., 13, 193–204 (2003).

    Article  Google Scholar 

  5. T. Roska and L. O. Chua, “Cellular neural networks with delay-type template elements and non-uniform grids,” Int. J. Circuit Theory Appl., 20, No. 4, 469–481 (1992).

    Article  MATH  Google Scholar 

  6. H. Zhao, “Global asymptotic stability of Hopfield neural network involving distributed delays,” Neural Networks, 17, 45–53 (2004).

    Article  Google Scholar 

  7. J. Zhang, “Absolute stability of a class of neural networks with unbounded delay,” Int. J. Circuit Theory Appl., 32, 11–21 (2004).

    Article  MATH  Google Scholar 

  8. J. Zhang, Y. Suda, and T. Iwasa, “Absolutely exponential stability of a class of neural networks with unbounded delay,” Neural Networks, 17, 391–397 (2003).

    Article  Google Scholar 

  9. J. Cao and J. Wang, “Global exponential stability and periodicity of recurrent neural networks with time delays,” IEEE Trans. Circuits Syst.-I, 52, 920–931 (2005).

    Article  MathSciNet  Google Scholar 

  10. J. Cao, “Global stability conditions for delayed CNNs,” IEEE Trans. Circuits and Syst.-I, 48, 1330–1333 (2001).

    Article  MATH  Google Scholar 

  11. H. Lu, F. Chung, and Z. He, “Some sufficient conditions for global exponential stability of delayed Hopfield neural networks,” Neural Networks, 17, 537–544 (2004).

    Article  MATH  Google Scholar 

  12. H. Jiang, Z. Li, and Z. Teng, “Boundedness and stability for autonomous cellular neural networks with delay,” Phys. Lett. A, 306, 313–325 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Rehim, H. Jiang, and Z. Teng, “Boundedness and stability for nonautonomous cellular neural networks with delay,” Neural Networks, 17, 1017–1025 (2004).

    Article  MATH  Google Scholar 

  14. J. Zhang, “Absolutely exponential stability in delayed cellular neural networks,” Int. J. Circuit Theory Appl., 30, 395–409 (2002).

    Article  MATH  Google Scholar 

  15. R. D. Driver, “Existence and stability of solutions of a delay-differential system,” Arch. Ration. Mech. Anal., 10, 401–426 (1962).

    Article  MATH  MathSciNet  Google Scholar 

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1401–1413, October, 2008.

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Loan, T.T., Tuan, D.A. Global exponential stability of a class of neural networks with unbounded delays. Ukr Math J 60, 1633–1649 (2008). https://doi.org/10.1007/s11253-009-0155-7

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  • DOI: https://doi.org/10.1007/s11253-009-0155-7

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