Abstract This paper investigates a series of harvesting problems of a harvested predator-prey system with Holling type IV functional response. The bionomic equilibrium, the maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system are studied. It is proved that the MSTY does not exist under the independent harvesting mode, while it may be found with the same predator and prey harvesting efforts mode. By applying the Bang-Bang control and the singular control to the harvesting strategy, the optimal equilibrium state of the discussed system converges faster than that of the system utilizing a single harvesting strategy with the fixed harvesting effort. The MISER 3 software package is adopted to obtain the optimization schemes of two control problems by using the control parameterization method. The findings of our study provide a theoretical basis for biological resource management.

中文翻译：

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具有 Holling IV 型功能响应的捕食者-猎物模型的最佳收获分析

摘要 本文研究了具有 Holling IV 型功能反应的捕食者-猎物系统的一系列收获问题。研究了该系统的生物组学平衡、最大可持续总产量（MSTY）和最优经济利润。证明在独立捕捞模式下不存在MSTY，而在捕食者和猎物捕捞努力模式相同的情况下可能会发现MSTY。通过将 Bang-Bang 控制和奇异控制应用于收获策略，所讨论系统的最佳平衡状态比使用固定收获努力的单一收获策略的系统收敛得更快。采用MISER 3软件包，利用控制参数化方法得到两个控制问题的优化方案。