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

Partha Sarathi Mandal and Malay Banerjee

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 4, 1216-1233

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.

Keywords: Beddington–DeAngelis functional response; Stability; Itô’s formula; Global solution; Persistence in mean; Stationary distribution (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (19)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:4:p:1216-1233

DOI: 10.1016/j.physa.2011.10.019

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