IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i16p2658-d1727146.html
   My bibliography  Save this article

General Decay Stability of Theta Approximations for Stochastic Delay Hopfield Neural Networks

Author

Listed:
  • Kai Liu

    (School of Science, Henan University of Engineering, Zhengzhou 451191, China)

  • Guodong Qin

    (School of Industrial Software, Henan University of Engineering, Zhengzhou 451191, China)

  • Linna Liu

    (School of Electric and Information Engineering, Zhongyuan University of Technology, Zhengzhou 451191, China)

  • Jumei Wei

    (School of Mathematics and Statistics, University of Zhengzhou, Zhengzhou 450001, China)

Abstract

This paper investigates the general decay stability of the stochastic linear theta (SLT) method and the split-step theta (SST) method for stochastic delay Hopfield neural networks. The definition of general decay stability for numerical solutions is formulated. Sufficient conditions are derived to ensure the general decay stability of the SLT and SST methods, respectively. The key findings reveal that, under the derived sufficient conditions, both the SLT and SST methods can achieve general decay stability when θ ∈ 1 2 , 1 , while for the case of θ ∈ 0 , 1 2 , the stability can also be guaranteed, which requires a stronger constraint on the step size. Finally, numerical examples are provided to demonstrate the effectiveness and validity of the theoretical results.

Suggested Citation

  • Kai Liu & Guodong Qin & Linna Liu & Jumei Wei, 2025. "General Decay Stability of Theta Approximations for Stochastic Delay Hopfield Neural Networks," Mathematics, MDPI, vol. 13(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2658-:d:1727146
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/16/2658/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/16/2658/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:gam:jmathe:v:13:y:2025:i:16:p:2658-:d:1727146. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.