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Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Ahmad, Bashir

Abstract

In this paper, we formulate and analyze a stochastic predator–prey model with additional food and nonlinear perturbation. Firstly, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution of the positive solution to the model. Then we obtain sufficient conditions for extinction of the predator species in two cases, one is the prey species surviving and the predator species extinction; the other is both the prey and predator species are extinct. Finally, some examples together with numerical simulations are provided to illustrate the analytical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:226-239
    DOI: 10.1016/j.amc.2017.09.030
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    References listed on IDEAS

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    1. Zhao, Dianli & Yuan, Sanling, 2016. "Dynamics of the stochastic Leslie–Gower predator–prey system with randomized intrinsic growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 419-428.
    2. Zhang, Xinhong & Li, Wenxue & Liu, Meng & Wang, Ke, 2015. "Dynamics of a stochastic Holling II one-predator two-prey system with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 571-582.
    3. Sahoo, Banshidhar & Poria, Swarup, 2014. "The chaos and control of a food chain model supplying additional food to top-predator," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 52-64.
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