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Stationary distribution of a stochastic ratio-dependent predator-prey system with regime-switching

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  • Wang, Zhaojuan
  • Deng, Meiling
  • Liu, Meng

Abstract

This article explores a stochastic ratio-dependent predator-prey model with regime-switching. We testify that the model admits a unique stationary distribution, and demonstrate that the transition probability of the solution of the model converges to the stationary distribution in exponent rate. We also discuss the biological implications of the results by aid of some numerical simulations.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308547
    DOI: 10.1016/j.chaos.2020.110462
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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. Ji, Chunyan & Jiang, Daqing & Fu, Jing, 2019. "Rich dynamics of a stochastic Michaelis–Menten-type ratio-dependent predator–prey system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    3. Liu, Meng & Bai, Chuanzhi, 2020. "Optimal harvesting of a stochastic mutualism model with regime-switching," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    4. Jingliang Lv & Ke Wang & Dongdong Chen, 2015. "Analysis on a Stochastic Two-Species Ratio-Dependent Predator-Prey Model," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 403-418, June.
    5. 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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    Cited by:

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    2. Juan Liu & Jie Hu & Peter Yuen & Fuzhong Li, 2022. "A Seasonally Competitive M-Prey and N-Predator Impulsive System Modeled by General Functional Response for Integrated Pest Management," Mathematics, MDPI, vol. 10(15), pages 1-15, July.
    3. Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    4. Lu, Chun & Liu, Honghui & Zhang, De, 2021. "Dynamics and simulations of a second order stochastically perturbed SEIQV epidemic model with saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Lu, Chun, 2022. "Dynamical analysis and numerical simulations on a crowley-Martin predator-prey model in stochastic environment," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    6. Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    7. Zhang, Shengqiang & Yuan, Sanling & Zhang, Tonghua, 2022. "A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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