IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v386y2020ics0096300320304252.html
   My bibliography  Save this article

Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process

Author

Listed:
  • Ayoubi, Tawfiqullah
  • Bao, Haibo

Abstract

The persistence and extinction (PE) are interesting topics in mathematics. This research analyzed PE of stochastic Logistic equations (SLE) by incorporating the Ornstein-Uhlenbeck process (SLOP) and stochastic delay Logistic equation (SDLE) by incorporating the Ornstein-Uhlenbeck process (SLDOP). Firstly, we proved that SLOP and SLDOP have positive solutions. Likewise, for stochastic permanence (SP), weak persistence in the mean (WPM), non-persistence in the mean (NPM) and extinction, the sufficient conditions are established for SLOP and SLDOP. Subsequently, for numerical simulation we used 4-stage stochastic Runge-Kutta (SRK4) to illustrate the effectiveness of the results.

Suggested Citation

  • Ayoubi, Tawfiqullah & Bao, Haibo, 2020. "Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304252
    DOI: 10.1016/j.amc.2020.125465
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320304252
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125465?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. Zhangzhi Wei & Zheng Wu & Ling Hu & Lianglong Wang, 2018. "Persistence and Extinction of a Stochastic Modified Bazykin Predator-Prey System with Lévy Jumps," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-7, April.
    2. Liu, Meng & Deng, Meiling & Du, Bo, 2015. "Analysis of a stochastic logistic model with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 169-182.
    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. Su, Tan & Yang, Qing & Zhang, Xinhong & Jiang, Daqing, 2023. "Stationary distribution, extinction and probability density function of a stochastic SEIV epidemic model with general incidence and Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    2. Wang, Haile & Zuo, Wenjie & Jiang, Daqing, 2023. "Dynamical analysis of a stochastic epidemic HBV model with log-normal Ornstein–Uhlenbeck process and vertical transmission term," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).
    4. Alfifi, H.Y., 2021. "Stability and Hopf bifurcation analysis for the diffusive delay logistic population model with spatially heterogeneous environment," Applied Mathematics and Computation, Elsevier, vol. 408(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. Liu, Meng & Bai, Chuanzhi, 2016. "Dynamics of a stochastic one-prey two-predator model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 308-321.
    2. Xiangjun Dai & Hui Jiao & Jianjun Jiao & Qi Quan, 2023. "Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions," Mathematics, MDPI, vol. 11(18), pages 1-19, September.
    3. Wang, Sheng & Hu, Guixin & Wei, Tengda & Wang, Linshan, 2020. "Permanence of hybrid competitive Lotka–Volterra system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Wang, Sheng & Wang, Linshan & Wei, Tengda, 2018. "Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 294-311.
    5. Sheng Wang & Linshan Wang & Tengda Wei, 2017. "Well-Posedness and Asymptotic Behaviors for a Predator-Prey System with Lévy Noise," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 715-725, September.

    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:apmaco:v:386:y:2020:i:c:s0096300320304252. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.