[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Finite-time stability of fractional-order bidirectional associative memory neural networks with mixed time-varying delays

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

This paper investigates the finite-time stability of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The sufficient conditions are derived to ensure the finite-time stability of systems by employing some analytical techniques and some inequalities. In addition, some conditions are achieved to guarantee the existence, the uniqueness and the finite-time stability of equilibrium point. Finally, two numerical examples are given to verify the effectiveness of the obtained main results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Ravichandran, C., Jothimani, K., Baskonus, H.M., Valliammal, N.: New results on nondensely characterized integrodifferential equations with fractional order. Eur. Phys. J. Plus. 133(109), 1–9 (2018)

    Google Scholar 

  2. Ravichandran, C., Logeswari, K., Jarad, F.: New results on existence in the framework of Atangana–Baleanu derivative for fractional integrodifferential equations. Chaos Solitons Fractals 125, 194–200 (2019)

    MathSciNet  Google Scholar 

  3. Song, C., Fei, S.M., Cao, J.D., Huang, C.X.: Robust synchronization of fractional-order uncertain chaotic systems based on output feedback sliding mode control. Mathematics 7, 599 (2019)

    Google Scholar 

  4. Ravichandran, C., Valliammal, N., Nieto, J.J.: New results on exact controllability of a class of fractional neutral integrodifferential systems with state-dependent delay in Banach spaces. J. Frankl. Inst. 356(3), 1535–1565 (2019)

    MATH  Google Scholar 

  5. Huang, C., Su, R., Cao, J.D.: Asymptotically stable high-order neutral cellular neural networks with proportional delays and D operators. Math. Comput. Simul. 171, 127–135 (2019)

    MathSciNet  Google Scholar 

  6. Xia, Y.H., Cao, J.D., Lin, M.R.: New results on the existence and uniqueness of almost periodic solutions for BAM neural networks with continuously distributed delays. Chaos Solitons Fractrals 31(4), 928–936 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Xia, Y.H.: Impulsive effect on the delayed Cohen–Grossberg-type BAM neural networks. Neurocomputing 73, 2754–2764 (2010)

    Google Scholar 

  8. Rajivganthi, C., Rihan, F.A., Lakshmanan, S., Rakkiyappan, R., Muthukumar, P.: Synchronization of memristor-based delayed BAM neural networks with fractional-order derivatives. Complexity 21, 412–426 (2016)

    MathSciNet  Google Scholar 

  9. Kosko, B.: Bidirectional associative memories. IEEE Trans. Sys. Man Cybern. 18, 49–60 (1988)

    MathSciNet  Google Scholar 

  10. Xiao, J.Y., Zhong, S.M., Li, Y.T., Xu, F.: Finite-time Mittag–Leffler synchronization of fractional-order memristive BAM neural networks with time delays. Neurocomputing 219, 431–439 (2017)

    Google Scholar 

  11. Ding, X.S., Cao, J.D., Zhao, X., Alsaadi, F.E.: Mittag–Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes. Proc. R. Soc. A. 473, 20170322 (2017)

    MathSciNet  MATH  Google Scholar 

  12. Zhang, B., Zhuang, J., Liu, H., et al.: Master-slave synchronization of a class of fractional-order Takagi-Sugeno fuzzy neural networks. Adv. Differ. Equ. 2018, 473 (2018). https://doi.org/10.1186/s13662-018-1918-y

    Article  MathSciNet  MATH  Google Scholar 

  13. Bao, H.B., Park, J.H., Cao, J.D.: Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn. 82(3), 1343–1354 (2015)

    MathSciNet  MATH  Google Scholar 

  14. Bao, H.B., Cao, J.D., Kurths, J.: State estimation of fractional-order delayed memristive neural networks. Nonlinear Dyn. 94(2), 1215–1225 (2018)

    Google Scholar 

  15. Hansan, S., Siong, N.K.: A parallel processing VLSI BAM engine. IEEE Trans. Neural Netw. 8, 424–436 (1997)

    Google Scholar 

  16. Acevedo-Mosqueda, M.E., Yanez-Marquez, C., Lopez-Yanez, I.: Alpha–Beta bidirectional associative memories: theory and applications. Neural Process. Lett. 26, 1–40 (2007)

    Google Scholar 

  17. Rajchakit, G., Pratap, A., Raja, R., Cao, J.D., Alzabut, J., Huang, C.X.: Hybrid control scheme for projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks with mixed delays. Mathematics 7, 759 (2019)

    Google Scholar 

  18. Cao, Y.P., Bai, C.Z.: Finite-time stability of fractional-order BAM neural networks with distributed delay. Abstr. Appl. Anal. 201, 634803 (2014)

    MathSciNet  MATH  Google Scholar 

  19. Zhang, L.H., Yang, Y.Q.: Different impulsive effects on synchronization of fractional-order memristive BAM neural networks. Nonlinear Dyn. 93, 233–250 (2018)

    MATH  Google Scholar 

  20. Bao, H.B., Park, J.H., Cao, D.: Non-fragile state estimation for fractional-order delayed memristive BAM neural networks. Neural Netw. 119, 190–199 (2019)

    Google Scholar 

  21. Ye, R.Y., Liu, X.S., Zhang, H., Cao, J.D.: Global Mittag–Leffler synchronization for fractional-order BAM neural networks with impulses and multiple variable delays via delayed-feedback control strategy. Neural Process. Lett. 49(1), 1–18 (2019)

    Google Scholar 

  22. Zhang, H., Ye, R.Y., Cao, J.D., Alsaedi, A.: Existence and globally asymptotic stability of equilibrium solution for fractional-order hybrid BAM neural networks with distributed delays and impulses. Complexity 2017, 6875874 (2017)

    MathSciNet  MATH  Google Scholar 

  23. Yang, X.J., Song, Q.K., Liu, Y.R., Zhao, Z.J.: Uniform stability analysis of fractional-order BAM neural networks with delays in the leakage terms. Abstr. Appl. Anal. 2014, 1–16 (2014)

    MathSciNet  MATH  Google Scholar 

  24. Wu, A.L., Zeng, Z.G., Song, X.G.: Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks. Neurocomputing. 177, 489–496 (2016)

    Google Scholar 

  25. Ke, Y.Q.: Finite-time stability of fractional order BAM neural networks with time delay. J. Discrete Math. Sci. Cryptogr. 20(3), 681–693 (2017)

    MathSciNet  Google Scholar 

  26. Wang, F., Yang, Y.Q., Xu, X.Y., Li, L.: Global asymptotic stability of impulsive fractional-order BAM neural networks with time delay. Neural Comput. Appl. 28, 345–352 (2017)

    Google Scholar 

  27. Rajivganthi, C., Rihan, F.A., Lakshmanan, S., Muthukumar, P.: Finite-time stability analysis for fractional-order Cohen–Grossberg BAM neural networks with time delays. Neural Comput. Appl. 29, 1309–1320 (2018)

    Google Scholar 

  28. Xu, C.J., Li, P.L., Pang, Y.C.: Finite-time stability for fractional-order bidirectional associative memory neural networks with time delays. Commun. Theor. Phys. 67, 137–142 (2017)

    MATH  Google Scholar 

  29. Ruan, S., Filfil, R.S.: Dynamics of a two-neuron system with discrete and distributed delays. Phys. D 191(3–4), 323–342 (2004)

    MathSciNet  MATH  Google Scholar 

  30. Wang, Z., Liu, Y., Liu, X.: On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345(4–6), 299–308 (2005)

    MATH  Google Scholar 

  31. Cao, J.D., Yuan, K., Li, H.X.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Netw. 17(6), 1646–1651 (2006)

    Google Scholar 

  32. Tyagi, S., Abbas, S., Hafayed, M.: Global Mittag-Leffler stability of complex-valued fractional-order neural network with discrete and distributed delays. Rend. Circ. Mat. Palermo 65(3), 1–21 (2016)

    MathSciNet  MATH  Google Scholar 

  33. Srivastava, H.M., Abbas, S., Tyagi, S., Lassoued, D.: Global exponential stability of fractional-order impulsive neural network with time-varying and distributed delay. Math. Methods Appl. Sci. 41, 2095–2104 (2018)

    MathSciNet  MATH  Google Scholar 

  34. Zhang, H., Ye, R.Y., Liu, S., Cao, J.D., Alsaedie, A., Li, X.D.: LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays. Int. J. Syst. Sci. 49, 1–9 (2018)

    MathSciNet  Google Scholar 

  35. Wu, H.Q., Zhang, X.X., Xue, S.H., Niu, P.F.: Quasi-uniform stability of Caputo-type fractional-order neural networks with mixed delay. Int. J. Mach. Learn. Cybern. 8(5), 1501–1511 (2017)

    Google Scholar 

  36. Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)

    MATH  Google Scholar 

  37. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Application of Fractional Differential Equations. Elsevier, NewYork (2006)

    MATH  Google Scholar 

  38. Li, C.P., Deng, W.H.: Remarks on fractional derivatives. Appl. Math. Comput. 182(2), 777–784 (2007)

    MathSciNet  MATH  Google Scholar 

  39. Mitrinovic, D.: Analytic Inequalities. Springer, Berlin (1970)

    MATH  Google Scholar 

  40. Willett, D.: Nonlinear vector integral equations as contraction mappings. Arch. Ration. Mech. Anal. 15, 79–86 (1964)

    MathSciNet  MATH  Google Scholar 

  41. Chen, L.P., Liu, C., Wu, R.C., He, Y.G., Chai, Y.: Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput. Appl. 27, 549–556 (2016)

    Google Scholar 

  42. Wu, R.C., Lu, Y.F., Chen, L.P.: Finite-time stability of fractional delayed neural networks. Neurocomputing 149, 700–707 (2015)

    Google Scholar 

  43. Yang, X.J., Song, Q.K., Liu, Y.R., Zhao, Z.J.: Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152, 19–26 (2015)

    Google Scholar 

  44. Zhuang, J.S., Cao, J.D., Tang, L.K., Xia, Y.H., Perc, M.: Synchronization analysis for stochastic delayed multi-layer network with additive couplings. IEEE Trans. Sys. Man Cybern. Sys. 99, 1–10 (2018)

    Google Scholar 

Download references

Acknowledgements

The first author would like to express her sincere gratitude to Professor Xiaoqun Wu (Wuhan University) for her kind help. The research is supported by the National Natural Science Foundation of China (Grant No. 11401595).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, 430074, Hubei, China

    Zhanying Yang, Jie Zhang & Yanqing Niu

Authors
  1. Zhanying Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanqing Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhanying Yang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Z., Zhang, J. & Niu, Y. Finite-time stability of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. J. Appl. Math. Comput. 63, 501–522 (2020). https://doi.org/10.1007/s12190-020-01327-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-020-01327-6

Keywords

Mathematics Subject Classification

Search

Navigation