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

Volume 10, Issue 12, pp 6205--6218

Publication Date: 2017-12-06

http://dx.doi.org/10.22436/jnsa.010.12.07

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 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.

Keywords

Service-resource mutualism model, white noise, Lévy jumps, persistence, optimal harvesting

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