广西红树林害虫综合防控数学模型研究

Mangrove is an important ecological system of the coastal wetland.But the insect pests affect the mangrove ecological balance seriously.According to the features and control measures of mangrove pests,this project uses the mathematical methods and numerical simulations on the development of mangrove pests to do the quantitative analysis and scientific forecast,so as to get the optimization program of the mangrove pest prevention and control.Firstly,using the qualitative and stability theory of ordinary differential equation to study the multi-stage mathematical model and the pest development rules are revealed .Secondly, using the theory of the differential equation and the comparison theorem and monotone iterative technique as well as inequality technique to study the mathematical models about trapping adults with light and the pest prevention and control strategy are obtained respectively for limited time and infinite time.Thirdly,using the comparison theorem of the impulse system and stroboscopic map as well as nonlinear analysis methods to study the mathematical model with impulsive effect,which is based on light trapping and combined with biological prevention and control. Then the strategy of integrated pest prevention and control is achieved.It can control the pests under the permitted threshold. Finally, using the theory of semi-continuous dynamical system to study the stage-structure mathematical model with state-dependent impulsive effect,analyzing the conditions of existence and stability of periodic solutions, and the optimal timing for mangrove pest prevention and control is acquired. This project provides the theoretical basis for the prevention and control of pests of mangrove and the scientific management of coastal wetland ecosystem.

红树林是海岸湿地十分重要的生态系统,其虫害严重影响红树林的生态平衡.本项目根据红树林害虫的特征和防控措施,利用数学方法和数值仿真模拟对红树林害虫的发展进行定量分析和科学预测,寻找红树林害虫防控最优化数量方案.首先应用常微分方程定性稳定性理论研究具有多个阶段结构的数学模型,揭示害虫的发展变化规律;其次,采用应用常微分方程的理论、比较定理、单调迭代技巧和不等式技巧研究夜间灯光诱杀成虫的数学模型,获得长期及短期灯光诱杀害虫的有效策略;然后运用脉冲系统的比较定理、频闪映射及非线性分析方法,研究在灯光诱杀基础上,结合生物防治进行综合害虫防控的具有脉冲效应的数学模型,获得将害虫控制在允许范围之内的综合防控策略;最后,运用半连续动力系统理论研究具有状态脉冲效应阶段结构的数学模型,分析周期解存在和稳定的条件,获得红树林害虫防控的最优化时机.本项目为红树林害虫的防控及海岸湿地生态系统的科学管理提供理论依据.

本项目围绕计划书中的研究内容和目标展开研究, 并完成研究计划. 项目根据红树林害虫的特征, 构建了几类描述物理防治、生物防治及两者组合的害虫防控的种群模型.利用微分方程和脉冲微分方程的理论、后继函数的方法、数学分析的方法及数值仿真模拟, 重点研究了具有脉冲效应的单种群系统、反馈脉冲控制比率依赖Leslie捕食者-食饵系统、状态反馈脉冲控制Holling-Tanner系统及状态反馈脉冲控制捕食者-食饵系统，获得这些种群系统周期解的存在性、稳定性及轨道稳定性, 进而获得物理防治与生物防治各种不同组合下将害虫控制在允许之内的害虫防控策略. 除此之外, 本项目研究了几类微分系统，研究了数据挖掘技术及数据挖掘技术在广西红树林虫害因素分析中的应用. 本研究创新了虫害防控的建模思想, 丰富了虫害防控模型的研究方法, 为红树林虫害预测预报和防治决策提供了可靠的数学依据.. 本项目获得了一些有意义的研究成果. 研究成果由22篇论文组成, 其中SCI/EI期刊论文6篇, 国内中文核心期刊论文9篇. 超额完成了预期指标.