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Global exponential stability analysis for cellular neural networks with variable coefficients and delays

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Abstract

Some sufficient conditions for the global exponential stability of cellular neural networks with variable coefficients and time-varying delays are obtained by a method based on a delayed differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of cellular neural networks with variable coefficients and time-varying delays. Some previous results in the literature are shown to be special cases of our results.

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References

  1. Clarke F, Ekeland I (1982) Nonlinear oscillations and boundary-value problems for Hamiltonian systems. Arch Rat Mech Anal 78: 315–333

    Article  MATH  MathSciNet  Google Scholar 

  2. Zhang Q, Wei X, Xu J (2003) Global exponential convergence analysis of delayed neural networks with time-varying delays. Phys Lett A 318: 537–544

    Article  MATH  MathSciNet  Google Scholar 

  3. Zhang Q, Wei X, Xu J (2005) On global exponential stability of delayed cellular neural networks with time-varying delays. Appl Math Comput 162:679–86

    Article  MATH  MathSciNet  Google Scholar 

  4. Zhang Q, Wei X, Xu J (2005) Delay-dependent exponential stability of cellular neural networks with time-varying delays. Chaos Solitons Fractals 23:1363–1369

    MATH  MathSciNet  Google Scholar 

  5. Gopalsamy K, He XZ (1994) Stability in asymmetric Hopfield nets with transmission delays. Physica D 76: 344–358

    Article  MATH  MathSciNet  Google Scholar 

  6. Driessche PVD, Zou X (1998) Global attractivity in delayed Hopfield neural networks models. SIAM J Appl Math 58:1878–1890

    Article  MATH  MathSciNet  Google Scholar 

  7. Chu T (2001) An exponential convergence estimate for analog neural networks with delay. Phys Lett A 283:113–118

    Article  MATH  MathSciNet  Google Scholar 

  8. Lu H (2000) On stability of nonlinear continuous-time neural networks with delays. Neural Netw 13:1135–1143

    Article  Google Scholar 

  9. Xu D, Zhao H, Zhu H (2001) Global dynamics of Hopfield neural networks involving variable delays. Comput Math Appl 42: 39–45

    Article  MATH  MathSciNet  Google Scholar 

  10. Liao X, Chen G., Sanchez EN (2002) LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans Circ Syst I 49:1033–1039

    Article  MathSciNet  Google Scholar 

  11. Joy M (2000) Results concerning the absolute stability of delayed neural networks. Neural Netw 13:613–616

    Article  Google Scholar 

  12. Zhou D, Cao J (2002) Globally exponential stability conditions for cellular neural networks with time-varying delays. Appl Math Comput 131:487–496

    Article  MATH  MathSciNet  Google Scholar 

  13. Chua LO, Yang L (1988) Cellular neural networks: theory and applications. IEEE Trans Circuits Syst 35:1257–1290

    Article  MATH  MathSciNet  Google Scholar 

  14. Kao Y, Gao C (2006) Global stability of bidirectional associative memory neural networks with variable coefficients and S-type distributed delays. LNCS 4232:598–607

    Google Scholar 

  15. Cao J, Wang J (2003) Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans Circuits Syst I 50:34–44

    Article  MathSciNet  Google Scholar 

  16. Zhang J (2003) Globally exponential stability of neural networks with variable delays. IEEE Trans Circuits Syst I 50:288–291

    Article  Google Scholar 

  17. Zhang Y, Zhong SM, Li ZL (1996) Periodic solutions and stability of Hopfield neural networks with variable delays. Int J Syst Sci 27:895–901

    Article  MATH  Google Scholar 

  18. Qiang Zhang, Xiaopeng Wei, Jin Xu (2006) Stability analysis for cellular neural networks with variable delays. Chaos Solitons Fractals 28:331–336

    Article  MATH  MathSciNet  Google Scholar 

  19. Berman A, Plemmons RJ (1979) Nonnegative matrices in the mathematical sciences. Academic, New York

    MATH  Google Scholar 

  20. Tokumarn H, Adachi N, Amemiya T (1975) Macroscopic stability of interconnected systems. In: 6th IFAC Congress Paper ID44.4, pp 1–7

  21. Hardy GH, Littlewood JE, Polya G (1952) Inequalities. 2nd edn. Cambridge University Press, London

    MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Editor and the anonymous reviewers for their valuable comments and constructive suggestions. Moreover, this work was supported by the National Natural Science Foundation of China under grant no. 60674020.

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Correspondence to Yonggui Kao.

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Kao, Y., Gao, C. Global exponential stability analysis for cellular neural networks with variable coefficients and delays. Neural Comput & Applic 17, 291–295 (2008). https://doi.org/10.1007/s00521-007-0121-y

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  • DOI: https://doi.org/10.1007/s00521-007-0121-y

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