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Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model

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  • Mandal, Partha Sarathi
  • Banerjee, Malay

Abstract

In this paper, we study a stochastic predator–prey model with Beddington–DeAngelis type functional response and logistic growth for predators. The deterministic model is already well-studied and we recall some important results here. We construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations. For the stochastic model, we show that the system admits unique positive global solution starting from the positive initial value. Then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes. Finally, we show that the system has a stationary distribution under certain parametric restrictions. Numerical simulations are carried out to substantiate the analytical results.

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  • Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1216-1233
    DOI: 10.1016/j.physa.2011.10.019
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    References listed on IDEAS

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    1. R. Mankin & T. Laas & E. Soika & A. Ainsaar, 2007. "Noise-controlled slow–fast oscillations in predator–prey models with the Beddington functional response," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 59(2), pages 259-269, September.
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    Cited by:

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    15. Jana, Debaldev & Banerjee, Aniket & Samanta, G.P., 2017. "Degree of prey refuges: Control the competition among prey and foraging ability of predator," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 350-362.
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