害虫综合治理与森林保护的数学模型研究

The invasion of harmful organisms makes it urgent to study the integrated pest management. The strategy applying biological control, chemical pesticides and physical control together is currently the most preferred. In this project, the mathematical model describing the interaction among plants with economical threshold, pests and their natural enemies in complex environment was established on the basis of experiments, observations and statistic data, to explore the optimal management strategy of the plants-pests-natural enemies' specie system. The properties of the system can be studied with the comprehensive way of thinking of modern mathematics and systems science, with the equilibrium state, periodic solutions, limit cycles, homoclinic orbits, heteroclinic orbits, stability and controllability of the system being discussed in phase space. Partial differential equations and optimization theory were applied to discuss the properties of the global solutions of the forest age structure-pest age structure nonlinear developing system, to study the existence of critical conditions for the steady state of the pest hazard system, optimal economical threshold, optimal release ratio of the natural enemies and other parameters, and to predict the reference data of spread, outbreak, forecast and prevention based on the actual data of the pest hazard. With the help of models and theoretical analysis methods to assess the impact of plant pests on forest protection, mathematical analysis of the forest protection and integrated pest management will be developed to provide a theoretical basis for the early discovery, prevention, control and strategies development.

有害生物的入侵为害虫的综合治理提出了迫切需要研究的课题，采用生物防治、化学农药和物理防治三者并用的策略是目前首选。本项目利用实验、观测和统计数据通过建立描述在复杂环境下具有经济阈值的植物、害虫和天敌相互作用的数学模型，探索植物- - 害虫- - 天敌三种群系统的最优管理策略。利用现代数学和系统科学综合性的思想方法研究系统的性质，在相空间讨论系统的平衡态、周期解、极限环、同宿轨、异宿轨、稳定性和可控性。利用偏微分方程和最优化理论探讨林龄结构和虫害年龄结构的非线性发展系统整体解的性质，研究病虫害系统状态稳定的临界条件、最优经济阈值和最优天敌投放比例等指标的存在性，根据有关病害实际数据预测预报其传播、爆发及进行预防控制的参考数据。借助模型和理论分析的方法评估植物害虫对森林保护的影响，旨在开展森林保护与害虫综合治理的数理分析，为病虫害的早期发现、预防控制和制定策略提供理论依据。

本项目利用害虫综合治理（物理防治、化学防治和生物防治）的思想，系统地建立了复杂环境下植物、害虫和天敌相互作用的病虫害数学模型，通过研究系统模型的平衡态、周期解、极限环、稳定性和可控性等性质，探索了植物- - 害虫- - 天敌三种群系统的最优防控策略。项目研究中建立了植物与害虫、害虫与天敌两种群微分方程模型，也建立了植物-害虫-天敌三种群系统模型，根据释放天敌和喷洒杀虫剂具有的脉冲效应，还建立了种群的脉冲微分方程模型，同时根据不同龄级植物的生长情况，建立并研究了带生长函数的考虑林龄因素的偏微分方程模型。利用现代数学和系统分析的方法，较系统地研究了这些微分方程模型的性质，根据多年来研究积累的森林病虫害高发区的实际数据资料，进行了一些病虫害的数值模拟，为早期预防和控制该病害提供了重要理论依据。本项目对森林病虫害进行的定量与定性应用基础研究，旨在当前还没有很有效防治该病虫害方法的情况下，利用数学方法对该病虫害的传播进行定量描述和系统分析，提供有效的预测和控制方法，为防治和根除该病虫害提供科学依据。