IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i9p1525-d807587.html
   My bibliography  Save this article

Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays

Author

Listed:
  • Lichao Feng

    (College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China)

  • Qiaona Wang

    (College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China)

  • Chunyan Zhang

    (College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China)

  • Dianxuan Gong

    (College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China)

Abstract

It is known that random noises have a significant impact on differential systems. Recently, the influences of random noises for impulsive systems have been started. Nevertheless, the existing references on this issue ignore the significant phenomena of nonlinear impulses and time-varying delays. Therefore, we see the necessity to study the influences of random noises for impulsive systems with the above two factors. Stimulated by the above, a polynomial random noise is introduced to suppress the potential explosive behavior of the nonlinear impulsive differential system with time-varying delay. Fortunately, the stochastically controlled impulsive delay differential system admits a unique global solution, is bounded, and grows at most in the polynomial form.

Suggested Citation

  • Lichao Feng & Qiaona Wang & Chunyan Zhang & Dianxuan Gong, 2022. "Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays," Mathematics, MDPI, vol. 10(9), pages 1-13, May.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1525-:d:807587
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/9/1525/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/9/1525/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    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. Xinsong Yang & Ruofeng Rao, 2023. "Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value," Mathematics, MDPI, vol. 11(10), pages 1-4, May.

    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. Abdelhamid Mohammed Djaouti & Zareen A. Khan & Muhammad Imran Liaqat & Ashraf Al-Quran, 2024. "A Study of Some Generalized Results of Neutral Stochastic Differential Equations in the Framework of Caputo–Katugampola Fractional Derivatives," Mathematics, MDPI, vol. 12(11), pages 1-20, May.
    2. Zhiguo Yan & Fangxu Su, 2022. "Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    3. Gautam, Pooja & Shukla, Anurag, 2023. "Stochastic controllability of semilinear fractional control differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Liu, Haoliang & Zhang, Taixiang & Li, Xiaodi, 2021. "Event-triggered control for nonlinear systems with impulse effects," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    5. Li, Huijuan & Li, Wuquan & Gu, Jianzhong, 2022. "Decentralized stabilization of large-scale stochastic nonlinear systems with time-varying powers," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    6. Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    7. He, Xinyi & Wang, Yuhan & Li, Xiaodi, 2021. "Uncertain impulsive control for leader-following synchronization of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    8. Dossan Baigereyev & Dinara Omariyeva & Nurlan Temirbekov & Yerlan Yergaliyev & Kulzhamila Boranbek, 2022. "Numerical Method for a Filtration Model Involving a Nonlinear Partial Integro-Differential Equation," Mathematics, MDPI, vol. 10(8), pages 1-24, April.
    9. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    10. Shukla, Anurag & Vijayakumar, V. & Nisar, Kottakkaran Sooppy, 2022. "A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1,2)," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    11. Lu Zhang & Caishi Wang & Jinshu Chen, 2023. "Interacting Stochastic Schrödinger Equation," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    12. Huang, Tao & Shao, Yiyu & Li, Liwei & Liu, Yajuan & Shen, Mouquan, 2024. "Guaranteed cost event-triggered H∞ control of uncertain linear system via output disturbance observer," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    13. Yuhan Chen & Chenliang Li, 2022. "A Tensor Splitting AOR Iterative Method for Solving a Tensor Absolute Value Equation," Mathematics, MDPI, vol. 10(7), pages 1-9, March.
    14. Chendur Kumaran, R. & Venkatesh, T.G. & Swarup, K.S., 2022. "Stochastic delay differential equations: Analysis and simulation studies," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    15. Yujuan Tian & Yuhan Yin & Fei Wang & Kening Wang, 2022. "Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties," Mathematics, MDPI, vol. 10(3), pages 1-14, February.

    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:10:y:2022:i:9:p:1525-:d:807587. 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.