IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i5p784-d1600997.html
   My bibliography  Save this article

Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching

Author

Listed:
  • Zhixian Zhang

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

  • Xiaoquan Ding

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

Abstract

Understanding the impact of unpredictable environmental fluctuations is crucial in population ecology because such fluctuations are an important feature of natural population systems. In this paper, we consider a stochastic single-species Kolmogorov system under Markovian switching. By using the Lyapunov method, we establish sufficient conditions for stochastic permanence, exponential ergodicity, and extinction of the system. Some examples are presented to illustrate corollaries, showing that our results generalize and improve on some known ones.

Suggested Citation

  • Zhixian Zhang & Xiaoquan Ding, 2025. "Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching," Mathematics, MDPI, vol. 13(5), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:784-:d:1600997
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/5/784/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/5/784/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ji, Weiming, 2019. "Permanence and extinction of a stochastic hybrid population model with Allee effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    2. Quan Wang & Li Zu & Daqing Jiang & Donal O’Regan, 2023. "Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching," Mathematics, MDPI, vol. 11(12), pages 1-17, June.
    3. Ruichao Li & Xiurong Guo, 2024. "Dynamics of a Stochastic SEIR Epidemic Model with Vertical Transmission and Standard Incidence," Mathematics, MDPI, vol. 12(3), pages 1-17, January.
    4. Li, Dagen & Liu, Meng, 2020. "Invariant measure of a stochastic food-limited population model with regime switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 16-26.
    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. Famei Zheng & Guixin Hu, 2022. "Dynamical Behaviors of a Stochastic Single-Species Model with Allee Effects," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1553-1563, September.
    2. Lu, Chun, 2021. "Dynamics of a stochastic Markovian switching predator–prey model with infinite memory and general Lévy jumps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 316-332.
    3. Wang, Zhaojuan & Deng, Meiling & Liu, Meng, 2021. "Stationary distribution of a stochastic ratio-dependent predator-prey system with regime-switching," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Yang, Huan & Tan, Yuanshun & Yang, Jin & Liu, Zijian, 2021. "Extinction and persistence of a tumor-immune model with white noise and pulsed comprehensive therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 456-470.

    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:13:y:2025:i:5:p:784-:d:1600997. 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.