带有恐惧和脉冲控制的捕食系统动力学分析

Dynamics Analysis of Predation System with Fear and Impulsive Control

摘要: 长期以来，化学农药是小麦蚜虫防治的主要手段。然而，随着小麦种植面积的增大，化学农药被大量使用，害虫抗药性增强、环境污染和生态破坏等问题日益突出。因此，寻找一种更加环保、可持续的防治方法成为当务之急。近年来，生物防治作为一种绿色环保的防治措施逐渐受到关注。使用生物防治手段可以保障农业安全，保护生态环境，从而推动农业可持续发展，促进农业科技创新。结合上述情况，建立一个数学模型来描述小麦生态系统，寻找合适便捷的调控手段，在环境污染无法根除的情况下保证小麦蚜虫的防治和小麦种植的持续健康发展具有十分重要的现实意义。建立状态反馈脉冲微分方程描述小麦蚜虫的防治过程，用脉冲策略来描述喷洒农药杀死小麦蚜虫和人工投放食蚜蝇幼虫，通过对状态反馈脉冲模型中阶一周期解的研究，将所得结论作为小麦蚜虫防治的理论基础，对小麦种植业的发展有重大的指导意义。

Abstract: For a long time, chemical pesticides have been the main means of controlling wheat aphids. However, with the expansion of wheat planting areas, the extensive use of chemical pesticides has led to increasingly prominent problems such as enhanced pest resistance, environmental pollution, and ecological damage. Therefore, finding a more environmentally friendly and sustainable control method has become an urgent task. In recent years, biological control, as a green and environmentally friendly control measure, has gradually attracted attention. The application of biological control methods can ensure agricultural safety, protect the ecological environment, and promote the sustainable development of agriculture and agricultural technological innovation. In light of the above situation, establishing a mathematical model to describe the wheat ecosystem and seeking appropriate and convenient control measures to ensure the control of wheat aphids and the sustainable and healthy development of wheat planting in the context of inevitable environmental pollution is of great practical significance. A state feedback impulsive differential equation is established to describe the process of controlling wheat aphids, and the impulsive strategy is used to describe the spraying of pesticides to kill wheat aphids and the artificial release of aphid larvae. Through the study of the first-order periodic solution in the state feedback impulsive model, the obtained conclusions can serve as the theoretical basis for the control of wheat aphids and have significant guiding significance for the development of the wheat planting industry.