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Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response

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  • Guirong Liu
  • Rong Liu

Abstract

This paper is concerned with a stochastic three-species food web model with omnivory which is defined as feeding on more than one trophic level. The model involves a prey, an intermediate predator, and an omnivorous top predator. First, by the stochastic comparison theorem, we show that there is a unique global positive solution to the model. Next, we investigate the asymptotic pathwise behavior of the model. Then, we conclude that the model is persistent in mean and extinct and discuss the stochastic persistence of the model. Further, by constructing a suitable Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Then, we present the application of the main results in some special models. Finally, we introduce some numerical simulations to support the main results obtained. The results in this paper generalize and improve the previous related results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:4876165
    DOI: 10.1155/2019/4876165
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    References listed on IDEAS

    as
    1. Liu, Rong & Liu, Guirong, 2019. "Analysis on stochastic food-web model with intraguild predation and mixed functional responses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    2. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Dynamical Behavior of a Stochastic Ratio-Dependent Predator-Prey System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, May.
    3. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    4. Richard J. Williams & Neo D. Martinez, 2000. "Simple rules yield complex food webs," Nature, Nature, vol. 404(6774), pages 180-183, March.
    5. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    6. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    7. 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.
    8. Ouyang, Mengqian & Li, Xiaoyue, 2015. "Permanence and asymptotical behavior of stochastic prey–predator system with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 539-559.
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    1. Melkikh, A.V. & Beregov, R.Y. & Sutormina, M.I., 2022. "Strange attractors and nontrivial solutions in games with three players," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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