In this paper, a pest management predator–prey model with weak Allee effect on predator and state feedback impulsive control on prey is introduced and analysed, where the yield of predator released and intensity of pesticide sprayed are assumed to be linearly dependent on the selected pest control level. For the proposed model, the existence and stability of the order-1 periodic orbit of the control system are discussed. Meanwhile, with the aim of minimizing the input cost in practice, an optimization model is constructed to determine the optimal quantity of the predator released and the intensity of pesticide sprayed. The theoretical results and numerical simulations indicated that the number of pests can be limited to below an economic threshold and displays periodic variation under the proposed control strategy. In addition, it indicated in numerical simulations that an order-2 periodic orbit exists for some certain parameters.

本文引入并分析了具有弱Allee效应的捕食者-捕食者模型和状态反馈对猎物的冲动控制，其中捕食者释放的产量和喷洒农药的强度被线性依赖于所选害虫控制级别。对于所提出的模型，讨论了控制系统的1阶周期轨道的存在性和稳定性。同时，为了在实践中将投入成本降至最低，构建了一个优化模型来确定捕食者释放的最佳数量和喷洒农药的强度。理论结果和数值模拟表明，在所提出的控制策略下，有害生物的数量可以限制在经济阈值以下，并显示出周期性变化。此外，