IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v372y2020ics0096300319309877.html
   My bibliography  Save this article

Synchronization for fractional-order discrete-time neural networks with time delays

Author

Listed:
  • Gu, Yajuan
  • Wang, Hu
  • Yu, Yongguang

Abstract

This paper is concerned with synchronization for fractional-order discrete-time neural networks (FDTNNs) without time delays and with time delays, respectively. First of all, the inequality on Riemann-Liouville fractional difference is proved in the light of the feather of the discrete function A(ν)(k), 0 < ν ≤ 1, which plays an important role in the investigation of the synchronization. Under the feedback controllers, synchronization conditions of FDTNNs without time delays and with time delays are derived by means of different techniques. Based on the inequality and the comparison principle of linear fractional difference system, the synchronization condition of FDTNNs without time delays is obtained. Further more, the synchronization condition of FDTNNs with time delays is derived through Lyapunov direct method with a suitable Lyapunov function involving discrete fractional sum term, which depends on the definition of Riemann-Liouville fractional difference. Lastly, simulations of two examples are provided to prove the effectiveness of the approaches.

Suggested Citation

  • Gu, Yajuan & Wang, Hu & Yu, Yongguang, 2020. "Synchronization for fractional-order discrete-time neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    • Handle: RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309877
    DOI: 10.1016/j.amc.2019.124995
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319309877
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.124995?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Park, Ju H., 2007. "Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1552-1559.
    2. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    3. Thabet Abdeljawad & Ferhan M. Atici, 2012. "On the Definitions of Nabla Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, October.
    4. Castañeda, Carlos E. & López-Mancilla, D. & Chiu, R. & Villafaña-Rauda, E. & Orozco-López, Onofre & Casillas-Rodríguez, F. & Sevilla-Escoboza, R., 2019. "Discrete-time neural synchronization between an Arduino microcontroller and a Compact Development System using multiscroll chaotic signals," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 269-275.
    5. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    6. Mohamad, S. & Gopalsamy, K., 2000. "Dynamics of a class of discrete-time neural networks and their continuous-time counterparts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(1), pages 1-39.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Ruoxia & Cao, Jinde & Xue, Changfeng & Manivannan, R., 2021. "Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Chen, Wei & Yu, Yongguang & Hai, Xudong & Ren, Guojian, 2022. "Adaptive quasi-synchronization control of heterogeneous fractional-order coupled neural networks with reaction-diffusion," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Zhao, Mingfang & Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun, 2023. "Quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks with time delays and uncertain parameters," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    4. Yuan, Xiaolin & Mo, Lipo & Yu, Yongguang & Ren, Guojian, 2021. "Containment control of fractional discrete-time multi-agent systems with nonconvex constraints," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    5. Yang, Zhanying & Zhang, Jie & Zhang, Zhihui & Mei, Jun, 2023. "An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 910-925.
    6. Zhang, Xiao-Li & Li, Hong-Li & Kao, Yonggui & Zhang, Long & Jiang, Haijun, 2022. "Global Mittag-Leffler synchronization of discrete-time fractional-order neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    7. Wang, Yangling & Cao, Jinde & Huang, Chengdai, 2024. "Bifurcations of a fractional three-layer neural network with different delays: Delay-dependent and order-dependent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    8. Cui, Xueke & Li, Hong-Li & Zhang, Long & Hu, Cheng & Bao, Haibo, 2023. "Complete synchronization for discrete-time fractional-order coupled neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. Wang, Mei & Jia, Baoguo & Chen, Churong & Zhu, Xiaojuan & Du, Feifei, 2020. "Discrete fractional Bihari inequality and uniqueness theorem of solutions of nabla fractional difference equations with non-Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 376(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yao, Yu & Wu, Li-Bing, 2022. "Backstepping control for fractional discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    2. Zhang, Xiao-Li & Li, Hong-Li & Kao, Yonggui & Zhang, Long & Jiang, Haijun, 2022. "Global Mittag-Leffler synchronization of discrete-time fractional-order neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    3. Liu, Xianggang & Ma, Li, 2020. "Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    4. Jiraporn Reunsumrit & Thanin Sitthiwirattham, 2020. "On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations," Mathematics, MDPI, vol. 8(4), pages 1-13, March.
    5. Xin, Baogui & Peng, Wei & Kwon, Yekyung, 2020. "A discrete fractional-order Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    6. Luo, Cheng & Liu, Bao-Qing & Hou, Hu-Shuang, 2021. "Fractional chaotic maps with q–deformation," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    7. Xu, Quan & Xu, Xiaohui & Zhuang, Shengxian & Xiao, Jixue & Song, Chunhua & Che, Chang, 2018. "New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 552-566.
    8. Burgos, C. & Cortés, J.-C. & Debbouche, A. & Villafuerte, L. & Villanueva, R.-J., 2019. "Random fractional generalized Airy differential equations: A probabilistic analysis using mean square calculus," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 15-29.
    9. Mohamad, Sannay, 2008. "Computer simulations of exponentially convergent networks with large impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 331-344.
    10. Liu, Xiang & Wang, Peiguang & Anderson, Douglas R., 2022. "On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    11. Park, Ju H., 2009. "Synchronization of cellular neural networks of neutral type via dynamic feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1299-1304.
    12. Qin, Xiaoli & Wang, Cong & Li, Lixiang & Peng, Haipeng & Yang, Yixian & Ye, Lu, 2018. "Finite-time modified projective synchronization of memristor-based neural network with multi-links and leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 302-315.
    13. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    14. Yang, Dan & Wang, JinRong & O’Regan, D., 2018. "A class of nonlinear non-instantaneous impulsive differential equations involving parameters and fractional order," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 654-671.
    15. Kaslik, E. & Balint, St., 2007. "Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1245-1253.
    16. Yang, Xiaofan & Liao, Xiaofeng & Megson, Graham M. & Evans, David J., 2005. "Global exponential periodicity of a class of neural networks with recent-history distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 441-447.
    17. Zhang, Shuo & Liu, Lu & Xue, Dingyu, 2020. "Nyquist-based stability analysis of non-commensurate fractional-order delay systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    18. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    19. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    20. Gao, Shigen & Wang, Yubing & Dong, Hairong & Ning, Bin & Wang, Hongwei, 2017. "Controlling uncertain Genesio–Tesi chaotic system using adaptive dynamic surface and nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 180-188.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309877. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.