Abstract
In this paper, a stochastic prey-predator model is investigated and analyzed, which possesses foraging arena scheme in polluted environments. Sufficient conditions are established for the extinction and persistence in the mean. These conditions provide a threshold that determines the persistence in the mean and extinction of species. Furthermore, it is also shown that the stochastic system has a periodic solution under appropriate conditions. Finally, several numerical examples are carried on to demonstrate the analytical results.
Z. Qiu is supported by the National Natural Science Foundation of China (NSFC) grant No. 12071217 and No. 11671206; T. Feng is supported by the Scholarship Foundation of China Scholarship Council grant No. 201806840120, the Postgraduate Research & Practice Innovation Program of Jiangsu Province grant No. KYCX18_0370 and the Fundamental Research Funds for the Central Universities grant No. 30918011339; X. Zhao is supported by the Scholarship Foundation of China Scholarship Council grant No. 201906840072
(Communicated by Michal Fečkan)
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