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为了控制害虫数量不超过一个确定的水平,引入具有阈值控制策略的非光滑的阶段结构的害虫增长模型,称之为Filippov系统.本文主要介绍和讨论了以成年种群数量作为指标的阈值控制策略.在此种情况下,分析了Filippov系统的滑动区域,滑线动力学以及真,假平衡态和伪平衡态的存在性.文章通过理论和数值方法讨论和证明了上述平衡态的稳定性.引入了具有生物应用意义的害虫控制,而得到的结论证明成年种群的数量通过阈值策略控制能够成功的稳定在经济阈值之下.
In order to control the number of pests not to exceed a certain level, a non-smooth pest growth model with threshold control strategy is introduced, which is called Filippov system.This paper mainly introduces and discusses the threshold control strategy using the index of adult population as index. In this case, the existence of sliding region, sliding line dynamics, true and false and pseudo-equilibrium states of Filippov system are analyzed.The stability and stability of the above equilibrium states are discussed and proved by theoretical and numerical methods. Biologically-controlled pest control, and the conclusion is obtained that the number of adult populations can be successfully stabilized below the economic threshold by threshold-based control.