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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.

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. [ABSTRACT FROM AUTHOR]

This work is concerned with a two-species stochastic state-switching competitive population model with distributed delays and harvesting. First, necessary and sufficient criteria for the existence of a unique ergodic stationary distribution of the system are established. Then necessary and sufficient criteria for the existence of the optimal harvesting policy are given, and the explicit expression of the optimal harvesting policy is obtained. Finally, some effects of the state-switching on the persistence, extinction and optimal harvesting strategy of the system are discussed with the help of several simulations. [ABSTRACT FROM AUTHOR]

This paper systematically investigates the optimal harvesting of a stochastic delay competitive Lotka–Volterra model with Lévy jumps. Under some simple assumptions, the sufficient conditions for extinction and stable in the time average of each species are established. The stability in distribution of this model is proved under our assumptions. Finally, the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained. And some numerical simulations are introduced to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

As well known that the sudden environmental shocks and toxicant can affect the population dynamics of fish species, a mechanistic understanding of how sudden environmental change and toxicant influence the optimal harvesting policy requires development. This paper presents the optimal harvesting of a stochastic two-species competitive model with Lévy noise in a polluted environment, where the Lévy noise is used to describe the sudden climate change. Due to the discontinuity of the Lévy noise, the classical optimal harvesting methods based on the explicit solution of the corresponding Fokker–Planck equation are invalid. The object of this paper is to fill up this gap and establish the optimal harvesting policy. By using of aggregation and ergodic methods, the approximation of the optimal harvesting effort and maximum expectation of sustainable yields are obtained. Numerical simulations are carried out to support these theoretical results. Our analysis shows that the Lévy noise and the mean stress measure of toxicant in organism may affect the optimal harvesting policy significantly. [ABSTRACT FROM AUTHOR]

In this paper an n-species stochastic delay competitive model with harvesting is proposed. Some dynamical properties of the model are considered. We first establish sufficient conditions for persistence in the mean of the species. Then asymptotic stability in distribution of the harvesting model is studied. Next the optimal harvesting effort and the maximum harvesting yield are given by using the ergodic approach. Finally the analytical results are illustrated through simulation figures using MATLAB followed by discussions and conclusions. [ABSTRACT FROM AUTHOR]