IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i1p155-d1312506.html
   My bibliography  Save this article

Generalized Halanay Inequalities and Asymptotic Behavior of Nonautonomous Neural Networks with Infinite Delays

Author

Listed:
  • Dehao Ruan

    (School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China)

  • Yao Lu

    (School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China)

Abstract

This paper focuses on the asymptotic behavior of nonautonomous neural networks with delays. We establish criteria for analyzing the asymptotic behavior of nonautonomous recurrent neural networks with delays by means of constructing some new generalized Halanay inequalities. We do not require to constructi any complicated Lyapunov function and our results improve some existing works. Lastly, we provide some illustrative examples to demonstrate the effectiveness of the obtained results.

Suggested Citation

  • Dehao Ruan & Yao Lu, 2024. "Generalized Halanay Inequalities and Asymptotic Behavior of Nonautonomous Neural Networks with Infinite Delays," Mathematics, MDPI, vol. 12(1), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:1:p:155-:d:1312506
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/1/155/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/1/155/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jiang, Haijun & Teng, Zhidong, 2006. "Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 83-93.
    2. Song, Qiankun & Zhao, Zhenjiang, 2005. "Global dissipativity of neural networks with both variable and unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 393-401.
    3. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2009. "Global exponential stability for nonautonomous cellular neural networks with unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1144-1151.
    Full references (including those not matched with items on IDEAS)

    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. Esteves, Salete & Oliveira, José J., 2015. "Global asymptotic stability of nonautonomous Cohen–Grossberg neural network models with infinite delays," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 333-346.
    2. Zhang, Guodong & Zeng, Zhigang, 2018. "Exponential stability for a class of memristive neural networks with mixed time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 544-554.
    3. Song, Qiankun & Wang, Zidong, 2008. "Neural networks with discrete and distributed time-varying delays: A general stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1538-1547.
    4. Jiang, Haijun & Teng, Zhidong, 2006. "Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 83-93.
    5. Ji, Yan & Lou, Xuyang & Cui, Baotong, 2009. "Global output convergence of Cohen–Grossberg neural networks with both time-varying and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 344-354.
    6. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    7. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    8. Cai, Liming & Li, Xuezhi & Yu, Jingyuan & Zhu, Guangtian, 2009. "Dynamics of a nonautonomous predator–prey dispersion–delay system with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2064-2075.
    9. Yang, Haifeng & Chu, Tianguang, 2007. "LMI conditions for stability of neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 557-563.
    10. Wang, Mei-Qi & Ma, Wen-Li & Li, Yuan & Chen, En-Li & Liu, Peng-Fei & Zhang, Ming-Zhi, 2022. "Dynamic analysis of piecewise nonlinear systems with fractional differential delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. Rakkiyappan, R. & Balasubramaniam, P., 2009. "LMI conditions for stability of stochastic recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1688-1696.
    12. Zhao, Weirui & Yan, Anzhi, 2009. "Stability analysis of neural networks with both variable and unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 697-707.
    13. Qian-hong Zhang & Li-hui Yang, 2012. "Dynamical analysis of fuzzy BAM neural networks with variable delays," Fuzzy Information and Engineering, Springer, vol. 4(1), pages 93-104, March.
    14. Lou, Xu Yang & Cui, Bao Tong, 2008. "Global robust dissipativity for integro-differential systems modeling neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 469-478.

    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:12:y:2024:i:1:p:155-:d:1312506. 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: 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.