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Existence and globally exponential stability of anti periodic solution for fuzzy BAM neural networks with time delays

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Abstract

By employing fundamental solution matrix of coefficients and Lyapunov function, we obtain some sufficient conditions on the existence and global exponential stability of anti periodic oscillatory solution for fuzzy bi-directional memory neural networks with time delays. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Finally an example illustrates our results are feasible.

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References

  1. Kosko, B.: Adaptive bi-directional associative memories. Appl. Opt. 26, 4947–4960 (1987)

    Article  Google Scholar 

  2. Kosko, B.: Bi-directional associative memories. IEEE Trans. Syst. Man Cybern. 18, 49–60 (1988)

    Article  MathSciNet  Google Scholar 

  3. Kosko, B.: Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, p. 38. Prentice-Hall, Englewood Cliffs (1992)

    MATH  Google Scholar 

  4. Samidurai, R., Sakthivel, R., Anthoni, S.M.: Global asymptotic stability of BAM neural networks with mixed delays and impulses. Appl. Math. Comput. 212(1), 113–119 (2009)

    MathSciNet  MATH  Google Scholar 

  5. Liu, B., Huang, L.: Global exponential stability of BAM neural networks with recent-history distributed delays and impulses. Neurocomputing 69(16–18), 2090–2096 (2006)

    Article  Google Scholar 

  6. Balasubramaniam, P., Kalpana, M., Rakkiyappan, R.: Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Math. Comput. Model. 53(5–6), 839–853 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cao, J., Wang, L.: Exponential stability and periodic oscilatory solution in BAM networks with delays. IEEE Trans. Neural Netw. 13, 457–463 (2002)

    Article  Google Scholar 

  8. Liu, B.: Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal. Real World Appl. 14(1), 559–566 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhao, L., Liu, P.: Global exponential stability and existence of periodic solution and anti-periodic solution for delayed Cohen–Grossberg BAM neural networks with impulse on time scales. Int. J. Pure Appl. Math. 62(3), 305–326 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Liao, X.F., Wong, K.W., Yang, S.Z.: Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays. Phys. Lett. A 316, 55–64 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lou, X., Cui, B., Wu, W.: On global exponential stability and existence of periodic solutions for BAM neural networks with distributed delays and reaction–diffusion terms. Chaos Solitons Fract. 36(4), 1044–1054 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cao, J., Jiang, Q.: An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays. Phys. Lett. A 330, 203–213 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Peng, S.: Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal. Real World Appl. 11(3), 2141–2151 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Xu, Y.: Periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Neural Process. Lett. 41(2), 293–307 (2014)

    Article  Google Scholar 

  15. Zhang, Z., Liu, K.: Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays. Neural Netw. 24(5), 427–439 (2011)

    Article  MATH  Google Scholar 

  16. Guo, S.J., Huang, L.H., Dai, B.X., Zhang, Z.Z.: Global existence of periodic solutions of BAM neural networks with variable coefficients. Phys. Lett. A 317, 97–106 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zheng, B., Zhang, Y., Zhang, C.: Global existence of periodic solutions on a simplified BAM neural network model with delays. Chaos Solitons Fractals 37(5), 1397–1408 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, Z., Zhou, D.: Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks. J. Frankl. Inst. 347(5), 763–780 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Tian, A., Gai, M., Shi, B., Zhang, Q.: Existence and exponential stability of periodic solution for a class of Cohen–Grossberg-type BAM neural networks. Neurocomputing 73(16–18), 3147–3159 (2010)

    Article  Google Scholar 

  20. Li, Y., Wang, C.: Existence and global exponential stability of almost periodic solutions for BAM neural networks with variable coefficients on time scales. Appl. Math. Model. 7, 2114–2120 (2012)

    MathSciNet  Google Scholar 

  21. Zhang, A., Qiu, J., She, J.: Existence and global exponential stability of periodic solution for high-order discrete-time BAM neural networks, Neural Netw. Off. J. Int. Neural Netw. Soc. 50(2), 98–109 (2013)

    MATH  Google Scholar 

  22. Zhang, W., Li, J., Chen, M.: Global exponential stability and existence of periodic solutions for delayed reaction–diffusion BAM neural networks with Dirichlet boundary conditions. Bound. Value Probl. 2013(1), 1501–1526 (2013)

    MathSciNet  MATH  Google Scholar 

  23. Ke, Y., Miao, C.: Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neural Comput. Appl. 23(3–4), 1089–1099 (2013)

    Google Scholar 

  24. Ge, J., Xu, J.: Computation of synchronized periodic solution in a BAM network with two delays. IEEE Trans. Neural Netw. 21(3), 439–450 (2010)

    Article  Google Scholar 

  25. Yang, W.: Existence of an exponential periodic attractor of periodic solutions for general BAM neural networks with time-varying delays and impulses. Appl. Math. Comput. 219(2), 569–582 (2012)

    MathSciNet  MATH  Google Scholar 

  26. Okochi, H.: On the existence of periodic solutions to nonlinear abstract parabolic equations. J. Math. Soc. Jpn. 40, 541–553 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  27. Al-Islam, N.S., Alsulami, S., Diagana, T.: Existence of weighted pseudo anti-periodic solutions to some non-autonomous differential equations. Appl. Math. Comput. 218, 6536–6548 (2012)

    MathSciNet  MATH  Google Scholar 

  28. Shi, P., Dong, L.: Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses. Appl. Math. Comput. 216, 623–630 (2010)

    MathSciNet  MATH  Google Scholar 

  29. Wei, X., Qiu, Z.: Anti-periodic solutions for BAM neural networks with time delays. Appl. Math. Comput. 221, 221–229 (2013)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  31. Yang, T., Yang, L., Wu, C., Chua, L.: Fuzzy cellular neural networks: theory. In: Proceedings of the IEEE International Workshop on Cellular Neural Networks Application, pp. 181–186 (1996)

  32. Yang, T., Yang, L., Wu, C., Chua, L.: Fuzzy cellular neural networks: applications. In: Proceedings of the IEEE International Workshop on Cellular Neural Neworks Application, pp. 225–230 (1996)

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  35. Zhang, Q., Xiang, R.: Global asymptotic stability of fuzzy cellular neural networks with time-varying delays. Phy. Lett. A 371, 3971–3977 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhang, Q., Yang, L., Liu, J.: Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen–Grossberge neural networks on time scales. Math. Slovaca 1(1), 119–138 (2015)

    MathSciNet  MATH  Google Scholar 

  37. Zhang, Q., Shao, Y., Liu, J.: Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays. Math. Methods Appl. Sci. 36(7), 773–779 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, Guizhou, People’s Republic of China

    Qianhong Zhang & Fubiao Lin

  2. Library, Guizhou University of Finance and Economics, Guiyang, 550025, Guizhou, People’s Republic of China

    Xiaoying Zhong

Authors
  1. Qianhong Zhang
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  2. Fubiao Lin
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  3. Xiaoying Zhong
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Correspondence to Qianhong Zhang.

Additional information

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 11361012, 11761018).

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Zhang, Q., Lin, F. & Zhong, X. Existence and globally exponential stability of anti periodic solution for fuzzy BAM neural networks with time delays. J. Appl. Math. Comput. 57, 729–743 (2018). https://doi.org/10.1007/s12190-017-1130-3

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  • DOI: https://doi.org/10.1007/s12190-017-1130-3

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