一类污染环境下随机渔业模型的最优收获

Optimal harvesting of a stochastic fishery model in a polluted environment

研究一类污染环境下受白噪声干扰的捕食-食饵渔业模型的最优收获策略。利用随机比较原理证明了全局正解的存在和唯一性,并应用伊藤公式讨论了鱼类种群的生存阈值;通过构造合适的Lyapunov函数,证明在一定条件下遍历平稳分布的存在唯一性。利用唯一不变概率测度的遍历性得到最优捕获努力量和最大预期持续产量的显式表达式。最后,进行数值模拟以支撑理论分析。结果表明,白噪声强度和污染物浓度对最大预期持续产量有副作用。

The optimal harvesting strategy of a predator-prey fishery model disturbed by white noise in a polluted environment is investigated.The existence and uniqueness of a globally positive solution are demonstrated using the principle of stochastic comparison,and the survival threshold of the fish population is discussed by applying Ito's formula.Under some certain conditions,the uniqueness of the existence of an ergodic stationary distribution is proved by constructing a suitable Lyapunov function.Explicit expressions of the optimal harvesting efforts and the maximum expected sustainable yield are obtained using the ergodicity property of the unique invariant probability measure.Finally,numerical simulations are performed to support the theoretical analysis.The results show that the intensity of white noise and pollutant concentration has a negative effect on the maximum expected sustainable yield.