Skip to main content
SpringerLink
Log in

Finite Time Synchronization of Delayed Quaternion Valued Neural Networks with Fractional Order

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this article, the finite time (FT) synchronization problem of fractional order quaternion valued neural networks with time delay is investigated. Without separating the quaternion valued system into two complex valued or four real valued systems, the FT synchronization conditions are derived through using Lyapunov direct method. Furthermore, the setting time is estimated, which is influenced by the order of fractional derivative and control parameters. Finally, numerical simulations are shown to verify the effectiveness of the proposed methods.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Ding ZX, Shen Y (2016) Global dissipativity of fractional-order neural networks with time delays and discontinuous activations. Neurocomputing 196:159–166

    Article  Google Scholar 

  2. Chen BSC, Chen JJ (2015) Global asymptotical \(\omega \)-periodicity of a fractional-order nonautonomous neural networks. Neural Netw 68:78–88

    Article  Google Scholar 

  3. Stamova I (2014) Global Mittag–Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays. Nonlinear Dyn 77:1251–1260

    Article  MathSciNet  Google Scholar 

  4. Yu J, Hu C, Jiang HJ (2012) \(\alpha \)-stability and \(\alpha \)-synchronization for fractional order neural networks. Neural Netw 35:82–87

    Article  Google Scholar 

  5. Rakkiyappan R, Cao JD, Velmurugan G (2015) Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays. IEEE Trans Neural Netw Learn Syst 26:84–97

    Article  MathSciNet  Google Scholar 

  6. Ding XS, Cao JD, Zhao X, Alsaadi FE (2017) Finite-time stability of fractional order complex-valued neural networks with time delays. Neural Process Lett 2:1–20

    Google Scholar 

  7. Peng X, Wu HQ, Song K, Shi JX (2017) Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays. Neural Netw 94:46–54

    Article  Google Scholar 

  8. Velmurugan G, Rakkiyappan R, Cao J (2016) Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Neural Netw 73:36–46

    Article  Google Scholar 

  9. Li HL, Cao JD, Jiang HJ, Alsaedi A (2018) Finite-time synchronization of fractional-order complex networks via hybrid feedback control. Neurocomputing 320:69–75

    Article  Google Scholar 

  10. Zheng BB, Hu C, Yu J, Jiang HJ (2020) Finite-time synchronization of fully complex-valued neural networks with fractional-order. Neurocomputing 373:70–80

    Article  Google Scholar 

  11. Xu Y, Li W (2020) Finite-time synchronization of fractional-order complex valued coupled systems. Physica A 549:123903

    Article  MathSciNet  Google Scholar 

  12. Matsui N, Isokawa T, Kusamichi H (2004) Quaternion neural network with geometrical operators. J Intell Fuzzy Syst 15:149–164

    MATH  Google Scholar 

  13. Zou CM, Kou KI, Wang YL (2016) Quaternion collaborative and sparse representation with application to color face recognition. IEEE Trans Signal Process 25:3287–3302

    MathSciNet  MATH  Google Scholar 

  14. Huang CD, Nie XB, Zhao X (2019) Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw 117:67–93

    Article  Google Scholar 

  15. Xiao JY, Zhong SM (2019) Synchronization and stability of delayed fractional order memristive quaternion-valued neural networks with parameter uncertainties. Neurocomputing 363:321–338

    Article  Google Scholar 

  16. Yang XJ, Li CD, Song QK (2018) Global Mittag–Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw 105:88–103

    Article  Google Scholar 

  17. Li H, Zhang L, Hu C, Jiang H, Cao J (2020) Global Mittag–Leffler synchronization of fractional-order delayed quaternion-valued neural networks: direct quaternion approach. Appl Math Comput 373:1–11

    MathSciNet  MATH  Google Scholar 

  18. Xiao J, Cao J, Cheng J, Zhong S, Wen S (2020) Novel methods to finite time Mittag–Leffler synchronization problem of fractional-order quaternion valued neural networks. Inf Sci 526:221–244

    Article  MathSciNet  Google Scholar 

  19. Li XF, Fang JA, Zhang WB, Li HY (2018) Finite-time synchronization of fractional-order memristive recurrent neural networks with discontinuous activation functions. Neurocomputing 316:284–293

    Article  Google Scholar 

  20. Podlubny I (1999) Fractional differential equations. Academic Press, New York, pp 88–95

    MATH  Google Scholar 

  21. Kilbas A, Srivastava H, Trujillo J (2006) Theory and applications of fractional differential equations. Elsevier, NewYork, pp 110–115

    MATH  Google Scholar 

  22. Kamenkov G (1953) On stability of motion over a finite interval of time. J Appl Math Mech 17:529–540

    MathSciNet  Google Scholar 

  23. Lin DY, Chen XF, Li B (2019) LMI conditions for some dynamical behaviors of fractional-order quaternion-valued neural networks. Adv Differ Equ 2019:1–29

    Article  MathSciNet  Google Scholar 

  24. Chen XF, Li ZS, Song QK (2017) Robust stability analysis of quaternion valued neural networks with time delays and parameter uncertainties. Neural Netw 91:55–65

    Article  Google Scholar 

  25. Butzer P, Westphal U (2000) An introduction to fractional calculus. World Scientific, Singapore, pp 86–94

    MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the project supported by the National Natural Science Foundation of China (Nos. 11971013 and 61807006), the Natural Science Foundation of Anhui Province (No. 1908085MA01)and the Natural Science Foundation of the Higher Education Institutions of Anhui Province (Nos. KJ2019A0573 and KJ2019A0556), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No.18KJD110001) and the Special Foundation for Young Scientists of Anhui Province (No. gxyq2019048).

Author information

Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Weiwei Zhang, Hongyong Zhao, Chunlin Sha & Yuan Wang

  2. School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, China

    Weiwei Zhang

  3. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 211106, China

    Hongyong Zhao

Authors
  1. Weiwei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongyong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chunlin Sha
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongyong Zhao.

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

Zhang, W., Zhao, H., Sha, C. et al. Finite Time Synchronization of Delayed Quaternion Valued Neural Networks with Fractional Order. Neural Process Lett 53, 3607–3618 (2021). https://doi.org/10.1007/s11063-021-10551-5

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-021-10551-5

Keywords

Search

Navigation