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Invariant measure of a stochastic food-limited population model with regime switching

Author

Listed:
  • Li, Dagen
  • Liu, Meng

Abstract

This paper puts forward and tests a food-limited population model with both white noise and regime switching perturbations. It is testified that there exists a key value ā, with the following features: if ā>0, then the model owns a unique ergodic invariant measure to which the transition probability of the solution converges exponentially fast; if ā<0, then the limit of the solution as time approaches infinity is zero. The results uncover that both white noise and regime switching could make the stability of the model change.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:16-26
    DOI: 10.1016/j.matcom.2020.06.003
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    References listed on IDEAS

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    1. Nguyen, Dang Hai & Yin, George & Zhu, Chao, 2017. "Certain properties related to well posedness of switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3135-3158.
    2. Liu, Meng & Bai, Chuanzhi, 2020. "Optimal harvesting of a stochastic mutualism model with regime-switching," Applied Mathematics and Computation, Elsevier, vol. 373(C).
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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).

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