IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v210y2023icp661-677.html
   My bibliography  Save this article

Persistence, Extinction, and boundedness in pth moment of hybrid stochastic logistic systems by delay feedback control based on discrete-time observation

Author

Listed:
  • Mukama, Denis Sospeter
  • Ghani, Mohammad
  • Mbalawata, Isambi Sailon

Abstract

This paper focuses on the study of long-term behaviour of the stochastic logistic systems under Markov chain using delay feedback control based on discrete-time observations. Necessary conditions for extinction, persistence and boundedness in pth moment of the species in the time average is examined. Particularly, the upper bound of (τ+τ0) of the time lag between two successive observations τ and the delay time τ0, is obtained. The stochastic comparison theorem and asymptotic analysis are the main techniques applied. It has been observed that, the delay feedback control has an impact on the persistence of the species. Synthetic examples and virtual realities are given to support the findings.

Suggested Citation

  • Mukama, Denis Sospeter & Ghani, Mohammad & Mbalawata, Isambi Sailon, 2023. "Persistence, Extinction, and boundedness in pth moment of hybrid stochastic logistic systems by delay feedback control based on discrete-time observation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 661-677.
    • Handle: RePEc:eee:matcom:v:210:y:2023:i:c:p:661-677
    DOI: 10.1016/j.matcom.2023.03.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423001398
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.03.034?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. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
    2. Geiß, Christel & Manthey, Ralf, 1994. "Comparison theorems for stochastic differential equations in finite and infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 23-35, September.
    3. Li, Dingshi, 2013. "The stationary distribution and ergodicity of a stochastic generalized logistic system," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 580-583.
    4. Hongxiao Hu & Ling Zhu, 2015. "Permanence and Extinction of Stochastic Logistic System with Feedback Control under Regime Switching," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-6, September.
    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. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Wu, Yongbao & Guo, Haihua & Li, Wenxue, 2020. "Finite-time stabilization of stochastic coupled systems on networks with Markovian switching via feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Zhang, Tian & Chen, Huabin, 2019. "The stability with a general decay of stochastic delay differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 294-307.
    4. Feng, Lichao & Liu, Qiumei & Cao, Jinde & Zhang, Chunyan & Alsaadi, Fawaz, 2022. "Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    5. Damir Filipović & Sander Willems, 2020. "A term structure model for dividends and interest rates," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1461-1496, October.
    6. Rajasekar, S.P. & Pitchaimani, M., 2019. "Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 207-221.
    7. Ding, Xiaodong & Wu, Rangquan, 1998. "A new proof for comparison theorems for stochastic differential inequalities with respect to semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 155-171, November.
    8. Yu, Peilin & Deng, Feiqi, 2022. "Stabilization analysis of Markovian asynchronous switched systems with input delay and Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    9. Wang, Tianxiao & Yong, Jiongmin, 2015. "Comparison theorems for some backward stochastic Volterra integral equations," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1756-1798.
    10. Li, Yuyuan & Lu, Jianqiu & Kou, Chunhai & Mao, Xuerong & Pan, Jiafeng, 2018. "Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 152-161.
    11. Luo, Tianjiao, 2019. "Stabilization of multi-group models with multiple dispersal and stochastic perturbation via feedback control based on discrete-time state observations," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 396-410.
    12. Gaston Clément Nyassoke Titi & Jules Sadefo-Kamdem & Louis Aimé Fono, 2021. "Optimal Renewable Resource Harvesting model using price and biomass stochastic variations: A Utility Based Approach," Working Papers hal-03169348, HAL.
    13. Zhou, Yaxin & Jiang, Daqing, 2023. "Dynamic behavior of infectious diseases influenced by TV and social media advertisement," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    14. Damir Filipovi'c & Sander Willems, 2018. "A Term Structure Model for Dividends and Interest Rates," Papers 1803.02249, arXiv.org, revised May 2020.
    15. Gaston Clément Nyassoke Titi & Jules Sadefo Kamdem & Louis Aimé Fono, 2022. "Optimal renewable resource harvesting model using price and biomass stochastic variations: a utility based approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 297-326, April.
    16. Wu, Zhen & Xu, Mingyu, 2009. "Comparison theorems for forward backward SDEs," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 426-435, February.
    17. Sun, Xinguo & Zuo, Wenjie & Jiang, Daqing & Hayat, Tasawar, 2018. "Unique stationary distribution and ergodicity of a stochastic Logistic model with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 864-881.
    18. Nguyen, Dang H. & Nguyen, Nhu N. & Yin, George, 2020. "General nonlinear stochastic systems motivated by chemostat models: Complete characterization of long-time behavior, optimal controls, and applications to wastewater treatment," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4608-4642.
    19. Song, Minghui & Geng, Yidan & Liu, Mingzhu, 2021. "Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    20. Zhang, Na & Jia, Guangyan, 2013. "Stochastic monotonicity and order-preservation for a type of nonlinear semigroups," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 422-429.

    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:matcom:v:210:y:2023:i:c:p:661-677. 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/mathematics-and-computers-in-simulation/ .

    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.