title: Analysis of a stochastic tri-trophic food-chain model with harvesting.
abstract: 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 depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic 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 existence of 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.
authors: School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, People's Republic of China. liumeng0557@sina.com.|School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People's Republic of China. liumeng0557@sina.com.
authors: Meng
authors: M
authors: Liu
authors: School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, People's Republic of China.
authors: Chuanzhi
authors: C
authors: Bai
mesh_terms: D004777:Environment; D020387:Food Chain; D008954:Models, Biological; D013269:Stochastic Processes
keywords: Management of natural resources; Optimization under uncertainties; Stochastic control