Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment

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.