IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v545y2020ics0378437119321065.html
   My bibliography  Save this article

Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps

Author

Listed:
  • Tan, Jianguo
  • Tan, Yahua
  • Guo, Yongfeng
  • Feng, Jianfeng

Abstract

In this paper, we main investigate the almost sure exponential stability of stochastic delay Hopfield neural networks with jumps on numerical solutions. The methods we used are Euler approach and backward Euler approach. By giving some conditions of theoretical significance, we verify that not only Euler approach but also backward Euler approach is almost sure exponential stability. However, the range of application of Euler approach is smaller than that of backward Euler approach. Moreover, our main research tool is the discrete semimartingale convergence theorem. Lastly, we give an example as illustration.

Suggested Citation

  • Tan, Jianguo & Tan, Yahua & Guo, Yongfeng & Feng, Jianfeng, 2020. "Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321065
    DOI: 10.1016/j.physa.2019.123782
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119321065
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123782?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. Rathinasamy, A. & Narayanasamy, J., 2019. "Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 126-152.
    2. Liu, Linna & Zhu, Quanxin, 2015. "Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 698-712.
    3. Hongyu Qin & Zhiyong Wang & Fumin Zhu & Jinming Wen, 2018. "Stability Analysis of Additive Runge-Kutta Methods for Delay-Integro-Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-5, June.
    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. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    2. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 438(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. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    3. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    4. Zhang, Chunmei & Han, Bang-Sheng, 2020. "Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    5. Li, Zhao-Yan & Shang, Shengnan & Lam, James, 2019. "On stability of neutral-type linear stochastic time-delay systems with three different delays," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 147-166.
    6. Wang, Fen & Chen, Yuanlong, 2021. "Mean square exponential stability for stochastic memristor-based neural networks with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Wan, Li & Zhou, Qinghua & Liu, Jie, 2017. "Delay-dependent attractor analysis of Hopfield neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 68-72.
    8. Rathinasamy, A. & Narayanasamy, J., 2019. "Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 126-152.
    9. Zhang, Huasheng & Zhuang, Guangming & Sun, Wei & Li, Yongmin & Lu, Junwei, 2020. "pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    10. Yu, Peilin & Deng, Feiqi & Sun, Yuanyuan & Wan, Fangzhe, 2022. "Stability analysis of impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    11. Liu, Zhiguang & Zhu, Quanxin, 2023. "Ultimate boundedness of impulsive stochastic delay differential equations with delayed impulses," Statistics & Probability Letters, Elsevier, vol. 199(C).
    12. Nie, Rencan & Cao, Jinde & Zhou, Dongming & Qian, Wenhua, 2019. "Analysis of pulse period for passive neuron in pulse coupled neural network," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 277-289.
    13. Zhifu Jia & Cunlin Li, 2023. "Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures," Mathematics, MDPI, vol. 11(14), pages 1-19, July.

    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:phsmap:v:545:y:2020:i:c:s0378437119321065. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.