Skip to main content
SpringerLink
Log in

Synchronization Analysis of Multi-Order Fractional Neural Networks Via Continuous and Quantized Controls

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, the synchronization of multi-order fractional neural networks (MoFNNs) with time-varying delays is investigated. Two kinds of controls, namely continuous control and quantized control, are introduced respectively to implement the synchronization. Moreover, by virtue of vector Lyapunov functions, sufficient criteria for realizing the synchronization of the MoFNNs with time-varying delays are deduced. The results of this paper cover the synchronization of traditional fractional neural networks with identical derivative order as a special case. Finally, a numerical example with two cases is given to verify the theoretical results.

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. Zhang H, Ye M, Ye R, Cao J (2018) Synchronization stability of Riemann-Liouville fractional delay-coupled complex neural networks. Phys A 508:155–165

    Article  MathSciNet  Google Scholar 

  2. Zhang H, Cheng J, Zhang H, Zhang W, Cao J (2021) Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays. Chaos Soliton Fract 152:111432

    Article  MathSciNet  Google Scholar 

  3. Aadhithiyan S, Raja R, Zhu Q, Alzabut J, Niezabitowski M, Lim CP (2021) Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control. Chaos Soliton Fract 147:110853

    Article  MathSciNet  Google Scholar 

  4. Perdikaris P, Karniadakis GE (2014) Fractional-order viscoelasticity in one-dimensional blood flow models. Ann Biomed Eng 42(5):1012–1023

    Article  Google Scholar 

  5. Allagui A, Freeborn TJ, Elwakil AS, Fouda ME, Maundy BJ, Radwan AG, Said Z, Abdelkareem MA (2018) Review of fractional-order electrical characterization of supercapacitors. J Power Sour 400:457–467

    Article  Google Scholar 

  6. Sierociuk D, Ziubinski P (2014) Fractional order estimation schemes for fractional and integer order systems with constant and variable fractional order colored noise. Circuits Syst Signal Process 33(12):3861–3882

    Article  MathSciNet  Google Scholar 

  7. Pu Y, Yi Z, Zhou J (2016) Fractional Hopfield neural networks: fractional dynamic associative recurrent neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2319–2333

    Article  MathSciNet  Google Scholar 

  8. Boroomand A, Menhaj MB (2009) On-line nonlinear systems identification of coupled tanks via fractional differential neural networks, in Proc. Guilin, China, Chin. Control Decision Conf., pp 2185–2189

  9. Aguilar CJZ, Gmez-Aguilar JF, Alvarado-Martnez VM, Romero-Ugalde HM (2020) Fractional order neural networks for system identification. Chaos Soliton Fract 130:109444

    Article  MathSciNet  Google Scholar 

  10. Shen J, Lam J (2016) Stability and performance analysis for positive fractional-order systems with time-varying delays. IEEE Trans Autom Control 61(9):2676–2681

    Article  MathSciNet  Google Scholar 

  11. Diethelm K, Siegmund S, Tuan HT (2017) Asymptotic behavior of solutions of linear multi-order fractional differential systems. Fract Calc Appl Anal 20(5):1165–1195

    Article  MathSciNet  Google Scholar 

  12. Gallegos JA, Duarte-Mermoud MA (2018) A dissipative approach to the stability of multi-order fractional systems. IMA J Math Control Inf 37(1):143–158

    MathSciNet  MATH  Google Scholar 

  13. Gallegos JA, Aguila-Camacho N, Duarte-Mermoud MA (2019) Smooth solutions to mixed-order fractional differential systems with applications to stability analysis. J Integral Equ Appl 31(1):59–84

    Article  MathSciNet  Google Scholar 

  14. Lenka BK (2019) Fractional comparison method and asymptotic stability results for multivariable fractional order systems. Commun Nonlin Sci Numer Simul 69:398–415

    Article  MathSciNet  Google Scholar 

  15. Jia J, Wang F, Zeng Z (2021) Global stabilization of fractional-order memristor-based neural networks with incommensurate orders and multiple time-varying delays: a positive-system-based approach, Nonlinear Dynam., 1-27

  16. Jmal A, Makhlouf AB, Nagy A, Naifar O (2019) Finite-time stability for Caputo-Katugampola fractional-order time-delayed neural networks. Neural Process Lett 50(1):607–621

    Article  Google Scholar 

  17. Liu P, Wang J, Zeng Z (2021) An overview of the stability analysis of recurrent neural networks with multiple equilibria. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3105519

    Article  Google Scholar 

  18. Xu C, Liu Z, Yao L, Aouiti C (2021) Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays. Appl Math Comput 410:126458

    MathSciNet  MATH  Google Scholar 

  19. Lin J, Xu R, Li L (2021) Mittag-Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control. Nonlinear Anal-Model 25(2):207–226

    Article  MathSciNet  Google Scholar 

  20. Tang Z, Park JH, Wang Y, Feng J (2020) Impulsive synchronization of derivative coupled neural networks with cluster-tree topology. IEEE Trans Netw Sci Eng 7(3):1788–1798

    Article  MathSciNet  Google Scholar 

  21. Zhang W, Zhang H, Cao J, Alsaadi FE, Chen D (2019) Synchronization in uncertain fractional-order memristive complex-valued neural networks with multiple time delays. Neural Netw 110:186–198

    Article  Google Scholar 

  22. Song X, Song S, Li B, Tejado Balsera I (2018) Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications. Trans Inst Meas Control 40(10):3078–3087

    Article  Google Scholar 

  23. Gu Y, Yu Y, Wang H (2017) Synchronization-based parameter estimation of fractional-order neural networks. Phys A 483:351–361

    Article  MathSciNet  Google Scholar 

  24. Fan Y, Huang X, Wang Z, Xia J, Shen H (2020) Quantized control for synchronization of delayed fractional-order memristive neural networks. Neural Process Lett 52:403–419

    Article  Google Scholar 

  25. Chang Q, Hu A, Yang Y, Li L (2020) The optimization of synchronization control parameters for fractional-order delayed memristive neural networks using siwpso. Neural Process Lett 51(2):1541–1556

    Article  Google Scholar 

  26. Liu P, Xu M, Sun J, Zeng Z (2020) On pinning linear and adaptive synchronization of multiple fractional-order neural networks with unbounded time-varying delays, IEEE Trans. Cybern

  27. Liu P, Zeng Z, Wang J (2018) Global synchronization of coupled fractional-order recurrent neural networks. IEEE Trans Neural Netw Learn Syst 30(8):2358–2368

    Article  MathSciNet  Google Scholar 

  28. Liu P, Zeng Z, Wang J (2020) Asymptotic and finite-time cluster synchronization of coupled fractional-order neural networks with time delay. IEEE Trans Neural Netw Learn Syst 31(11):4956–4967

    Article  MathSciNet  Google Scholar 

  29. Liu P, Kong M, Xu M, Sun J, Liu N (2020) Pinning synchronization of coupled fractional-order time-varying delayed neural networks with arbitrary fixed topology, Neurocomputing,

  30. Ye R, Liu X, Zhang H, Cao J (2019) 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

    Article  Google Scholar 

  31. Lu W, Chen T (2004) Synchronization of coupled connected neural networks with delays. IEEE Trans Circuits Syst 51(12):2491–2503

    Article  MathSciNet  Google Scholar 

  32. Zhu Q (2018) Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Trans Automat Contr 64(9):3764–3771

    Article  MathSciNet  Google Scholar 

  33. Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, The Netherlands

    MATH  Google Scholar 

  34. Aguila-Camacho N, Duarte-Mermoud MA, Gallegos JA (2014) Lyapunov functions for fractional order systems. Commun Nonlinear Sci Numer Simul 19(9):2951–2957

    Article  MathSciNet  Google Scholar 

  35. Kang Y, Qin J, Ma Q, Gao H, Zheng W (2018) Cluster synchronization for interacting clusters of nonidentical nodes via intermittent pinning control. IEEE Trans Neural Netw Learn Syst 29(5):1747–1759

    Article  MathSciNet  Google Scholar 

  36. Wang H, Yu Y, Wen G, Zhang S, Yu J (2015) Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154:15–23

    Article  Google Scholar 

  37. Liang S, Wu R, Chen L (2016) Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay. Phys A 444:49–62

    Article  MathSciNet  Google Scholar 

  38. Kong F, Zhu Q (2021) New fixed-time synchronization control of discontinuous inertial neural networks via indefinite Lyapunov-Krasovskii functional method. Int J Robust Nonlin 31:471–495

    Article  MathSciNet  Google Scholar 

  39. Kong F, Zhu Q, Huang T (2021) New fixed-time stability lemmas and applications to the discontinuous fuzzy inertial neural networks. IEEE Trans Fuzzy Syst 29(12):3711–3722

    Article  Google Scholar 

  40. Xu C, Yang X, Lu J, Feng J, Alsaadi FE, Hayat T (2017) Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cybern 48(10):3021–3027

    Article  Google Scholar 

  41. Bao H, Park JH, Cao J (2021) Adaptive synchronization of fractional-order output-coupling neural networks via quantized output control. IEEE Trans Neural Netw Learn Syst 32(7):3230–3239

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China under (62076222; 61703313), the Key Scientific Research Project of Universities of Henan Province of China (21A120009), and the Scientific and Technological Project of Henan Province of China (202102310203; 202102310284)

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, Henan, China

    Minglin Xu, Peng Liu, Feifei Yang, Na Liu & Junwei Sun

Authors
  1. Minglin Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feifei Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Na Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Junwei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peng Liu.

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

Xu, M., Liu, P., Yang, F. et al. Synchronization Analysis of Multi-Order Fractional Neural Networks Via Continuous and Quantized Controls. Neural Process Lett 54, 3641–3656 (2022). https://doi.org/10.1007/s11063-022-10778-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-022-10778-w

Keywords

Search

Navigation