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Analysis of global exponential stability and periodic solutions of FCNNs with constant delays and time-varying delays

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Abstract

In this paper, we investigate a class of fuzzy cellular neural networks with constant delays and time-varying delays. By constructing suitable Lyapunov functional and employing Young inequality, we find sufficient conditions for the existence, uniqueness, global exponential stability of equilibrium, and the existence of periodic solutions of fuzzy cellular neural networks with time-varying delays. The results of this paper are new and they extend previously known results.

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References

  1. Chua, L.O., Yang, L.: Cellular neural networks: Theory. IEEE Trans. Circuits Syst. I 35, 1257–1272 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chua, L.O., Yang, L.: Cellular neural networks: Application. IEEE Trans. Circuits Syst. I 35, 1273–1290 (1988)

    Article  MathSciNet  Google Scholar 

  3. Cao, J.D.: Global stability analysis in delayed cellular networks. Phys. Rev. E 59, 5940–5944 (1999)

    Article  MathSciNet  Google Scholar 

  4. Cao, J.D., Zhou, D.M.: Stability analysis of delayed cellular neural networks. Neural Netw. 11, 1601–1605 (1998)

    Article  Google Scholar 

  5. Li, X.M., Huang, L.H., Zhu, H.Y.: Global stability of cellular neural networks with constant and variable delays. Nonliner Anal. 23, 319–333 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Huang, H., Cao, J.D., Wang, J.: Global stability and periodic solutions of recurrent neural networks with delays. Phys. Lett. A 298, 393–404 (2002)

    MathSciNet  MATH  Google Scholar 

  7. Cao, J.D.: New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys. Lett. A 307, 136–147 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhang, J.Y.: Global stability analysis in delayed cellular neural networks. Comput. Math. Appl. 45, 1707–1720 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang, J.Y.: Absolute stability analysis in cellular neural networks with variable delays and unbounded delay. Comput. Math. Appl. 47, 183–194 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jiang, H.J., Teng, Z.D.: Global exponential stability of cellular neural networks with time-varing coeffiences and delays. Neural Netw. 17, 1415–1425 (2004)

    Article  MATH  Google Scholar 

  11. Huang, T.W., Cao, J.D., Li, C.D.: Necessary and sufficient condition for the absolute exponential stability of a class of neural networks with finite delay. Phys. Lett. A 352, 94–98 (2006)

    Article  MATH  Google Scholar 

  12. Yang, T., Yang, L.B.: The global stability of fuzzy cellular neural networks. IEEE Trans. Circuits Syst. I 43, 880–883 (1996)

    Article  Google Scholar 

  13. Yang, T., Yang, L.B., Wu, C.W., Chua, L.O.: Fuzzy cellular neural networks: theory. In: Proc. IEEE Int. Workshop Cellular Neural Networks Appl., pp. 181–186 (1996)

  14. Huang, T.W.: Exponential stability of fuzzy cellular neural networks with distributed delay. Phys. Lett. A 351, 48–52 (2006)

    Article  MATH  Google Scholar 

  15. Liu, Y.Q., Tang, W.S.: Exponential stability of fuzzy cellular neural networks with constant and time-varying delays. Phys. Lett. A 323, 224–233 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yuan, K., Cao, J.D., Deng, J.M.: Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing 69, 1619–1627 (2006)

    Article  Google Scholar 

  17. Huang, T.W.: Exponential stability of delayed fuzzy cellular neural networks with diffusion. Chaos Solitons Fractals 31, 658–664 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, Q.H., Luo, W.: Global exponential stability and periodic solution of FCNNs with constant delays and time-varying delays. In: International Joint Conference on Computational Sciences and Optimization, pp. 659–662 (2009)

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Authors and Affiliations

  1. Guizhou Key Laboratory of Economic System Simulation, Guizhou College of Finance and Economics, Guiyang, Guizhou, 550004, P.R. China

    Qianhong Zhang

  2. Basic Science Department, Hunan Institute of Technology, Hengyang, Hunan, 421002, P.R. China

    Qianhong Zhang & Wei Luo

  3. Department of Mathematics, Hunan City University, Yiyang, Hunan, 413000, P.R. China

    Lihui Yang

Authors
  1. Qianhong Zhang
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  2. Wei Luo
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  3. Lihui Yang
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Corresponding author

Correspondence to Qianhong Zhang.

Additional information

This work is partially supported by the Scientific Research Foundation of Hunan Provincial Education Department (10B023) and supported by the Doctoral Foundation of Guizhou College of Finance and Economics.

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Zhang, Q., Luo, W. & Yang, L. Analysis of global exponential stability and periodic solutions of FCNNs with constant delays and time-varying delays. J. Appl. Math. Comput. 37, 459–471 (2011). https://doi.org/10.1007/s12190-010-0444-1

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  • DOI: https://doi.org/10.1007/s12190-010-0444-1

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