In this article, stochastic differential equations are used to model the dynamics of a harvested population in the presence of weak Allee effects. Two optimal harvesting policies are presented, one with variable effort based on optimal control theory, which is for practical reasons inapplicable in a random environment, and the other with constant effort and easily applicable. For a logistic‐like model with weak Allee effects, we show that the optimal policy based on constant effort implies, in a suitable range of effort values, the existence of a steady‐state stochastic equilibrium with a stationary density, obtained explicitly here, for the population size. With this new result, we compare the performance of both policies in terms of the profit obtained over a finite time horizon. Using realistic data from a harvested population and a logistic‐type growth model, we quantify the profit reduction when choosing the optimal policy based on constant effort instead of the optimal policy based on variable effort. We also study the influence of the Allee effects strength.

中文翻译：

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随机微分方程收获策略：Allee效应，类似逻辑的增长和利润优化

在本文中，随机微分方程用于在弱Allee效应下模拟收获种群的动态。提出了两种最优的采伐策略，一种是基于最佳控制理论的可变努力，由于实际原因，该策略不适用于随机环境，另一种则是恒定的努力且易于应用。对于具有弱Allee效应的类似Logistic的模型，我们证明了基于恒定努力的最优策略意味着在一个适当的努力值范围内，存在一个固定密度的稳态随机均衡，在此明确获得，用于人口规模。有了这个新结果，我们就在有限的时间范围内获得的利润方面比较了两种策略的性能。从收获人口和物流型增长模式使用真实的数据，我们基于不断的努力，而不是基于可变努力的最优政策选择最佳的策略时，量化的利润减少。我们还研究了Allee效应强度的影响。