外来物种传播模型及预测研究

发布时间：2018-06-20 09:16

本文选题：外来物种 + 微分方程　；参考：《浙江工业大学》2017年硕士论文

【摘要】：本文主要利用数学建模的思想方法研究外来入侵物种的综合治理问题。建立外来入侵物种的微分方程模型,讨论系统平衡点的存在性和稳定性,并根据实际情况进行数值模拟,为综合治理外来入侵物种提供有力的理论依据。第三章主要针对外来入侵的松材线虫病害,利用种群动力学的研究方法,考虑使用化学药剂等因素,将所有的松树分为三类(易感类、染病类、免疫类),建立单种群三仓室微分方程模型。利用稳定性的第一近似方法讨论系统正平衡点的存在性与稳定性,同时根据染病树木数量讨论了虫害的时变传播率。第四章利用数值分析的方法,一方面对第三章的理论结果进行了数值模拟,验证了结论的正确性;另一方面,根据千岛湖等地虫害实际,根据不同的传播率和不同的移除系数对松材线虫害的传播进行了预测预报,对时变有效传播率也进行了计算。计算结果显示,降低有效传播率β和增大移除系数h能在治理松材线虫害时起到积极作用。第五章根据海南省引进天敌姬小蜂和啮小蜂来治理外来物种椰心叶甲的案例,首先考虑了椰心叶甲、椰子树和椰心叶甲的天敌三种群的相互关系,建立了三种群微分方程模型;其次分别对模型的无天敌平衡点和有天敌平衡点的存在性和稳定性进行了证明;最后进行的数值分析表明,利用椰心叶甲的天敌姬小蜂和啮小蜂进行生物防治的效果比单靠化学药物治理椰心叶甲虫害效果更好。
[Abstract]:In this paper, mathematical modeling is used to study the comprehensive management of invasive alien species. The differential equation model of alien invasive species is established, the existence and stability of equilibrium point of the system are discussed, and the numerical simulation is carried out according to the actual situation, which provides a powerful theoretical basis for the comprehensive management of invasive alien species. The third chapter mainly aims at the invasion of pine wood nematode disease by using population dynamics research method, considering the use of chemical agents and other factors, all pine trees are divided into three categories (susceptible, infected, infected). The differential equation model of single population and three chambers was established. The existence and stability of the positive equilibrium point of the system are discussed by using the first approximation method of stability, and the time-varying propagation rate of pests is discussed according to the number of infected trees. The fourth chapter uses the numerical analysis method, on the one hand carries on the numerical simulation to the third chapter theory result, verifies the conclusion correctness; on the other hand, according to the thousand island lake and other places pest practice, According to the different propagation rate and different removal coefficient, the propagation of pine wood line pest was forecasted and the time-varying effective propagation rate was calculated. The results show that reducing effective propagation rate 尾 and increasing removal coefficient h can play an active role in controlling pine wood line pest. In the fifth chapter, according to the case of the introduction of natural enemy Jieji and Ephylla to control the alien species of Coconut leaf beetle in Hainan Province, the relationship among three populations of Coconut leaf beetle, coconut tree and natural enemy of Coconut leaf beetle is considered at first, and the differential equation model of three species is established. Secondly, the existence and stability of the natural enemy free equilibrium point and the natural enemy equilibrium point of the model are proved respectively. The effect of biological control by using natural enemy of Coconut leaf beetle, Apodemus hirsuta and Erythopsis roxburghii, is better than that of using chemical drugs alone to control the insect pest of Coconut leaf beetle.
【学位授予单位】：浙江工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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