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Analysis on a Stochastic Two-Species Ratio-Dependent Predator-Prey Model

Author

Listed:
  • Jingliang Lv

    (Harbin Institute of Technology (Weihai))

  • Ke Wang

    (Harbin Institute of Technology (Weihai))

  • Dongdong Chen

    (Harbin Institute of Technology (Weihai))

Abstract

A stochastic two-species ratio-dependent predator-prey system is investigated. We show that there is a unique positive solution to the model for any positive initial value. Stochastically ultimate boundedness and uniform continuity are considered. Moreover, under some conditions, we conclude that the stochastic model is persistent in mean and extinct. Finally we introduce some figures to illustrate our main results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9383-2
    DOI: 10.1007/s11009-013-9383-2
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    References listed on IDEAS

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    1. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

    1. Guirong Liu & Rong Liu, 2019. "Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response," Complexity, Hindawi, vol. 2019, pages 1-19, November.
    2. 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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