IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v404y2021ics0096300321002885.html
   My bibliography  Save this article

On boundedness and projective synchronization of distributed order neural networks

Author

Listed:
  • Mahmoud, Gamal M.
  • Aboelenen, Tarek
  • Abed-Elhameed, Tarek M.
  • Farghaly, Ahmed A.

Abstract

In this work, we introduced the distributed-order neural networks (DONNs) which are the generalization of integer and fractional orders neural networks. We presented and proved two theorems for bounded solutions and solutions that approach zero of these networks. The Gronwall–Bellman lemma, the asymptotical expansion of the generalized Mittag–Leffler function and Laplace transform are used to prove these theorems. We derived analytically the condition under which the solution of this network (DONN) is bounded. The active control and Lyapunov direct methods are applied to study the projective synchronization between two different chaotic DONNs. The analytical control functions are derived to achieve our synchronization. Two different examples of DONNs are given to test the validity of the analytical results of our theorems. The projective synchronization is investigated. Numerical simulations are implemented to show the agreement between both analytical and numerical results.

Suggested Citation

  • Mahmoud, Gamal M. & Aboelenen, Tarek & Abed-Elhameed, Tarek M. & Farghaly, Ahmed A., 2021. "On boundedness and projective synchronization of distributed order neural networks," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321002885
    DOI: 10.1016/j.amc.2021.126198
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321002885
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126198?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. Junhai Luo & Guanjun Li & Heng Liu, 2014. "Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, August.
    2. Guo-Hui, Li, 2005. "Synchronization and anti-synchronization of Colpitts oscillators using active control," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 87-93.
    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. Ali, Hegagi Mohamed & Ameen, Ismail Gad & Gaber, Yasmeen Ahmed, 2024. "The effect of curative and preventive optimal control measures on a fractional order plant disease model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 496-515.
    2. Abed-Elhameed, Tarek M. & Mahmoud, Gamal M. & Elbadry, Motaz M. & Ahmed, Mansour E., 2023. "Nonlinear distributed-order models: Adaptive synchronization, image encryption and circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Yang, Dongsheng & Yu, Yongguang & Wang, Hu & Ren, Guojian & Zhang, Xiaoli, 2024. "Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 178(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. El-Dessoky, M.M., 2009. "Synchronization and anti-synchronization of a hyperchaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1790-1797.

    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:404:y:2021:i:c:s0096300321002885. 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.