Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting


Authors

Hui Wang - School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China. Chenxi Du - School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China. Meng Liu - School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China. - School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China.


Abstract

In this paper, we propose a stochastic service-resource mutualism model with Lévy noises and harvesting. Under some assumptions, we study several dynamical properties of the model. We first obtain the thresholds between persistence and extinction for both the service species and the resource species. Then we give sharp sufficient conditions for stability in distribution of the model. Finally, we establish sufficient and necessary criteria for the existence of the optimal harvesting policy. The optimal harvesting effort and maximum of sustainable yield are also obtained. Our results reveal that the persistence, extinction, stability in distribution and optimal harvesting strategy have close relationships with the random noises.


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