害虫综合治理与森林保护的数学模型研究

项目名称： 害虫综合治理与森林保护的数学模型研究

项目编号： No.61273016

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 王定江

作者单位： 浙江工业大学

项目金额： 60万元

中文摘要： 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。

中文关键词： 病虫害；综合治理；森林保护；数学模型；系统分析

英文摘要： 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 a

英文关键词： Pest and disease；comprehensive management；forest protection；mathematical model；system analysis