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Finite-Time Synchronization for Fuzzy Delayed Neutral-Type Inertial Bam Neural Networks Via the Figure Analysis Approach

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Abstract

This paper focuses on the finite-time synchronization for fuzzy delayed neutral-type inertial BAM neural networks. Without making the variable transformation, the inertial system was analyzed directly. By applying integral inequality techniques and the figure analysis approach, some novel criteria are achieved to assure the finite-time synchronization between the drive system and the response system. The inequalities used in our paper are different from these in the existing papers. The figure analysis approach used to research finite-time synchronization in our paper is a completely novel study approach.

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References

  1. Babcock, K.L., Westervelt, R.M.: Stability and dynamics of simple electronic neural networks with added inertia. Physica D 23, 464–469 (1986)

    Article  Google Scholar 

  2. Zhang, Z.Q., Quan, Z.Y.: Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151, 1316–1326 (2015)

    Article  Google Scholar 

  3. Yu, S.H., Zhang, Z.Q., Quan, Z.Y.: New global exponential stability conditions for inertial Cohen-Grossberg neural networks with time delays. Neurocomputing 151, 1446–1454 (2015)

    Article  Google Scholar 

  4. Cui, N., Jiang, H.J., Hu, C., Abdurahman, A.: Global asymptotic and robust stability of inertial neural networks with proportional delays. Neurocomputing 272, 326–333 (2018)

    Article  Google Scholar 

  5. Zhang, W., Huang, T.W., He, X., Li, C.D.: Global exponential stability of inertial memristor-based neural networks with time-varying delays and impulses. Neural Netw. 95, 102–109 (2017)

    Article  Google Scholar 

  6. Ouyang, D.Q., Shao, J., Hu, C.: Stability property of impulsive inertial neural networks with unbounded time delay and saturating actuators. Neural Comput. Appl. https://doi.org/10.1007/s00521-019-04115-x

  7. Shi, M., Guo, J., Fang, X.W., Huang, C.X.: Global exponential stability of delayed inertial competitive neural networks. Adv. Differ. Equ. 2020:87 (2020)

  8. Liao, H.Y., Zhang, Z.Q., Ren, L., Peng, W.L.: Global asymptotic stability of periodic solutions for inertial delayed BAM neural networks via novel computing method of degree and inequality techniques. Chaos Solitons Fractals 104, 785–797 (2017)

    Article  MathSciNet  Google Scholar 

  9. Ke, Y.Q., Mian, C.F.: Anti-periodic solutions of inertial neural networks with time delays. Neural Process. Lett. 45, 523–538 (2017)

    Article  Google Scholar 

  10. Huang, C.X., Zhang, H.: Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method. Int. J. Biomath. 12(2), 1950016 (2019)

    Article  MathSciNet  Google Scholar 

  11. Huang, C.X., Yang, L.S., Liu, B.W.: New results on periodicity of nonautonomous inertial neural networks involving non-reduced order method. Neural Process. Lett. 50(1), 595–606 (2019)

    Article  Google Scholar 

  12. Du, B.: Anti-periodic solutions problem for inertial competitive neutral-type neural networks via wirtinger inequality. J. Inequal. Appl. 2019, 187 (2019)

    Article  MathSciNet  Google Scholar 

  13. Huang, C.X., Zhang, H.: Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method. Int. J. Biomath. 12(02), 1950016 (2019)

    Article  MathSciNet  Google Scholar 

  14. Kong, F.C., Zhu, Q.X., Wang, K., Nieto, J.J.: Stability analysis of almost periodic solutions of discontinuous BAM neural networks with hybrid time-varying delays and D operator. J. Franklin Inst. 356, 11605–11637 (2019)

    Article  MathSciNet  Google Scholar 

  15. Zhang, Z.Q., Ren, L.: New sufficient conditions on global asymptotic synchronization of inertial delayed neural networks by using integrating inequality techniques. Nonlinear Dyn. 95, 905–917 (2019)

    Article  Google Scholar 

  16. Tang, Q., Jian, J.G.: Exponential synchronization of inertial neural networks with mixed time-varying delays via periodically intermittent control. Neurocomputing 338, 181–190 (2019)

    Article  Google Scholar 

  17. Wan, P., Sun, D.H., Chen, D., Zhao, M., Zheng, L.J.: Exponential synchronization of inertial reaction-diffusion coupled neural networks with proportional delay via periodically intermittent control. Neurocomputing 356, 195–205 (2019)

    Article  Google Scholar 

  18. Rakkiyappan, R., Gayathri, D., Velmurugan, G.: Exponential synchronization of inertial memristor-based neural networks with time delay using average impulsive interval approach. Neural Process. Lett. (2019) https://doi.org/10.1007/s11063-019-09982-y

  19. Zhang, Z.Q., Cao, J.D.: Novel finite-time synchronization criteria for inertial neural networks with time delays via integral inequality method. IEEE Trans. Neural Netw. Learn. Syst. 30(5):1476–1483 (2019)

  20. Alimi, A.M., Aouiti, C.K., Assali, E.A.: Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and lit application to secure communication. Neurocomputing 332, 29–43 (2019)

    Article  Google Scholar 

  21. Guo, Z.Y., Gong, S.Q., Huang, T.W.: Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control. Neurocomputing 293, 100–107 (2018)

    Article  Google Scholar 

  22. Zhang, Z.Q., Chen, M., A, L. Li, , : Further study on finite-time synchronization for delayed inertial neural networks via inequality skills. Neurocomputing 373, 15–23 (2020)

    Article  Google Scholar 

  23. Zhou, F.Y., Yao, H.X.: Stability analysis for neutral-type inertial BAM neural networks with time-varying delays. Nonlinear Dyn. 92, 1583–1598 (2018)

    Article  Google Scholar 

  24. Zhang, Z.Q., Liu, W.B., Zhou, D.M.: Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays. Neural Netw. 25(1), 94–105 (2012)

    Article  Google Scholar 

  25. Zhang, Z.Q., Liu, K.Y., Yang, Y.: New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type. Neurocomputing 81, 24–32 (2012)

    Article  Google Scholar 

  26. Liu, G., Yang, S.X.: Stability criteria for BAM neural networks of neutral-type with interval time-varying delays. Proc. Eng. 15(1), 2836–2840 (2011)

    Article  Google Scholar 

  27. Zhang, Z.Q., Cao, J.D., Zhou, D.M.: Novel LMI based condition on global asymptotic stability for a class of Cohen-Grossberg BAM networks with extended activation functions. IEEE Trans. Neural Netw. Learn. Syst. 25(6), 1161–1172 (2014)

    Article  Google Scholar 

  28. Zhang, Z.Q., Lin, F.: Global Asymptotic stability of periodic solutions for neutral-type delayed BAM neural networks by combining an abstract theorem of k-set contractive operator with LMI method. Neural Process. Lett. https://doi.org/10.1007/s11063-018-90141-2

  29. Yang, T., Yang, L.B., Wu, C.W., Chua, L.O.: Fuzzy cellular neural networks: theory. In: Proceeding of the 1996 4th IEEE International Workshop on Cellular Neural Networks, and Their Applications, CNNA, 96, 181–186 (June 1996)

  30. Tyagi, S., Martha, S.C.: Finite-time stability for a class of fractional-order fuzzy neural networks with proportional delay. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2019.04.010

  31. Ali, M.S., Balasubramaniam, P., Rihan, F.A.: Stability criteria for stochastic takagi-sugeno fuzzy Cohen-Grossberg BAM neural networks with mixed time-varying delays. Complexity 21(5), 143–154 (2016)

    Article  MathSciNet  Google Scholar 

  32. Meng, F.R., Li, K.L., Zhao, Z.J., Song, Q.K., Liu, Y.R., Alsaadi, F.E.: Periodicity of impulsive Cohen-Grossberg-type fuzzy neural networks with hybrid delays. Neurocomputing 368, 153–162 (2019)

    Article  Google Scholar 

  33. Duan, L., Wei, H., Huang, L.H.: Finite-time synchronization of delayed fuzzy cellular neural networks with discontinuous activations. Fuzzy Sets Syst. 361, 56–70 (2019)

    Article  MathSciNet  Google Scholar 

  34. Jia, R.W.: Finite-time stability of a class of fuzzy cellular neural networks with multi-proportional delays. Fuzzy Sets Syst. 319, 70–80 (2017)

    Article  MathSciNet  Google Scholar 

  35. Wang, W.T.: Finite-time synchronization for a class of fuzzy cellular neural networks with time-varying coefficients and proportional delays. Fuzzy Sets Syst. 338, 40–49 (2018)

    Article  MathSciNet  Google Scholar 

  36. Jian, J.G., Wan, P.: Global exponential convergence of fuzzy complex-valued neural networks with time-varying delays and impulsive effects. Fuzzy Sets Syst. 338, 23–39 (2018)

    Article  MathSciNet  Google Scholar 

  37. Li, Y.K., Wang, C.: Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses. Fuzzy Sets Syst. 217, 62–79 (2013)

    Article  MathSciNet  Google Scholar 

  38. Bao, H.M.: Existence and exponential stability of periodic solution for BAM fuzzy Cohen-Grossberg neural networks with mixed delays. Neural Process. Lett. 43, 871–885 (2016)

    Article  Google Scholar 

  39. Jian, J.G., Duan, L.Y.: Finite-time synchronization for fuzzy neutral-type inertial neural networks with time-varying coefficients and proportional delays. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2019.04.004

  40. Abdurahman, A., Jiang, H.J., Teng, Z.D.: Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst. 297:96–111 (2016)

  41. Zheng, M.W., Li, L.X., Peng, H.P., Xiao, J.H., Yang, Y.X., Zhang, Y.P., Zhao, H.: Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks, Commun. Nonlinear Sci. Numer. Simul. 59, 272–291 (2018)

    Article  MathSciNet  Google Scholar 

  42. Zhang, Z.Q., Cao, J.D.: Finite-time synchronization for fuzzy inertial neural networks by maximum-value approach. IEEE Trans. Fuzzy Syst. https://doi.org/10.1109/TFUZZ22.2021.3059953.

  43. Kong, F.C., Zhu, Q.X., Sakthivel, R., Mohammadzadeh, A.: Fixed-time synchronization analysis for discontinuous fuzzy inertial neural networks with parameter uncertainties. Neurocomputing 422, 295–313 (2021)

    Article  Google Scholar 

  44. Duan, L., Shi, M., Huang, L.H.: New results on finite-/fixed-time synchronization of delayed diffusive fuzzy HNNS with discontinuous activations. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2020.04.016

  45. Kong, F.C., Zhu, Q.X., Huang, T.W.: New fixed-time stability Lemmas and applications to the discontinuous fuzzy inertial neural networks. IEEE TRans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.3026030

  46. Zhou, Y., Wan, X.X., Huang, C.X., Yang, X.S.: Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control. Appl. Math. Comput. 376, 125157 (2020)

  47. Wang, Q., Duan, L., Wei, H., Wang, L.: Finite-time anti-synchronization of delayed Hopfied neural networks with discontinuous activations. Int. J. Control. https://doi.org/10.10180/00207179.2021.1912396

  48. Pan, J.S., Zhang, Z.Q.: Finite-time synchronization for delayed complex-valued neural networks via the exponential-type controllers of time variable. Chaos Solitons Fractals 146, 110897 (2021)

  49. Ren, F.M., Jiang, M.H., Xu, H., Li, M.Q.: Quasi fixed-time synchronization of memristive Cohen-Grossberg neural networks with reaction-diffusion. Neurocomputing 415, 74–83 (2020)

    Article  Google Scholar 

  50. Ren, F.M., Jiang, M.H., Xu, H., Fang, D.: New finite-time synchronization of memristive Cohen-Grossberg neural networks with reaction-diffusion term based on time-varying delay. Neural Comput. Appl. (2020). https://doi.org/10.1007/s00521-020-05259-x

    Article  Google Scholar 

  51. Zhang, Z.Q., Li, A.L., Yu, S.H.: Finite-time synchronization for delayed complex-valued neural networks via integrating inequality method. Neurocomputing 318, 248–260 (2018)

    Article  Google Scholar 

  52. Zhang, Z.Q., Zheng, T., Yu, S.H.: Finite-time anti-synchronization of neural networks with time-varying delays via inequality skills. Neurocomputing 356, 60–68 (2019)

    Article  Google Scholar 

  53. Tang, Y.: Terminal sliding model control for rigid robots. Automatica 34, 51–56 (1998)

    Article  MathSciNet  Google Scholar 

  54. Yang, W.B.: Test site 600 and Test Site 700: Caokao Mathematics (Science). Foreign Language Testing and Research Press, Beijing (2016)

    Google Scholar 

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Correspondence to Zheng Zhou or Zhengqiu Zhang.

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Zhou, Z., Zhang, Z. & Chen, M. Finite-Time Synchronization for Fuzzy Delayed Neutral-Type Inertial Bam Neural Networks Via the Figure Analysis Approach. Int. J. Fuzzy Syst. 24, 229–246 (2022). https://doi.org/10.1007/s40815-021-01132-8

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  • DOI: https://doi.org/10.1007/s40815-021-01132-8

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