具有瞬时与非瞬时脉冲效应害虫治理切换模型的动力学性质分析

Analysis on the Dynamics of a Switching Pest Management Model with Instantaneous and Non-instantaneous Pulse Effects

将害虫种群分为幼虫和成虫两个阶段,假设成虫在固定时刻产卵,考虑到杀虫剂在喷洒瞬间大量杀死害虫之后,仍对害虫产生一个非瞬时的残留作用,建立具有瞬时与非瞬时脉冲效应的一类生育脉冲害虫治理切换模型.利用Jury判据等理论分析得到害虫种群灭绝或种群持续生存的阈值条件.最后,利用数值模拟分析了系统的动力复杂性,并给出了影响害虫种群灭绝或持续生存阈值的关键参数.

The pest population is divided into two stages: larva and adult.It is assumed that the adults lay eggs at the fixed times.Considering that the pesticides still have a non-instantaneous residual effects on the pests after a large amount of pests are killed at the moment of spraying, a birth pulse pest management switching model with instantaneous and non-instantaneous pulse effects is established.By using Jury criterion and theoretical analysis, the threshold condition for pest population extinction or persistence is obtained.Finally, numerical simulations are used to analyze the dynamical complexity of the system, and the key parameters affecting the extinction or persistent survival threshold of the pest population are given.