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Analysis of a stochastic tri-trophic food-chain model with harvesting. (English) Zbl 1347.92067
Summary: We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depend on the demographic impacts of environmental stochasticity on the species and species’ at lower trophic levels. However, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for the existence of an optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model.

MSC:
92D25 Population dynamics (general)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E20 Optimal stochastic control
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