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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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).
    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.
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