The aim of this paper is to study an optimal control problem for a non-autonomous model with one predator and two prey species, one strong and the other weak. The resulting model incorporates a weak Allee effect in the strong prey, seasonal breeding in both preys, and an extra-food supply. The model takes into account the death rate of predators, which results in a decrease in their biomass. We prove the existence, uniqueness, and qualitative properties of the solutions. The optimal control problem aims to control the predator population by considering three strategies. Simulation results show the usefulness and efficacy of the proposed control measures to manage the predator biomass.

中文翻译：

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具有强猎物和弱猎物的捕食者-猎物模型的最优控制问题


本文的目的是研究一个非自主模型的最佳控制问题，该模型具有一个捕食者和两个猎物物种，一个强，另一个弱。由此产生的模型在强猎物中结合了弱 Allee 效应，在两种猎物中加入了季节性繁殖，并增加了食物供应。该模型考虑了捕食者的死亡率，这导致它们的生物量减少。我们证明了解决方案的存在性、唯一性和定性特性。最优控制问题旨在通过考虑三种策略来控制捕食者种群。模拟结果表明，所提出的控制措施对管理捕食者生物量的有用性和有效性。