Abstract
The aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.
Highlights
As is well known, over-harvesting and unreasonable harvesting policies could cause a number of adverse effects, such as ecological destruction, species extinction, and desertification
It is very interesting to study the optimal harvesting of a competitive model
3 Stability in distribution we study the stability in distribution of model (1)
Summary
Over-harvesting and unreasonable harvesting policies could cause a number of adverse effects, such as ecological destruction, species extinction, and desertification. The optimal harvesting problem is a meaningful and significant topic in biology and mathematics (Zou and Wang [1]). Several scholars have paid attention to investigating competitive systems and obtained a lot of successful results (see, e.g., [2,3,4]) in recent years. Wang et al [5] have studied stability for the distribution of a stochastic competitive Lotka–Volterra system with S-type distributed time delays. It is very interesting to study the optimal harvesting of a competitive model. The typical competitive model with harvesting can be described as follows:
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