害虫综合防治建模驱动“半连续动力系统理论”兴起

以害虫综合防治数学建型为启迪,对生物数学研究的一些相关问题开展了一系列的研究.从实际问题出发,我们分别建立了"常微分方程模型"以及对应的"周期脉冲控制模型";随着害虫综合防治常态化管理和环境污染常态化防治的兴起,我们建立了"状态脉冲反馈控制系统"模型,简称"半连续动力系统"模型,提出了"半连续动力系统"相关的概念,创建了其基本理论,并且作了系统性的研究,例如:半连续动力系统的周期解以及周期解的稳定性、同宿轨和同宿分支、异宿轨和异宿分支以及"双边控制系统"等概念及其判定定理的研究;进一步将"半连续动力系统"相应的理论和方法应用于生物数学其他方面的一些相关问题的研究.本文以数学模型为载体,归纳总结了近十多年来对生物数学的研究历程,指出了当前研究中尚待解决的问题.

Modeling of Integrated Pest Control Drives the Rise of"Semi-continuous Dynamical System Theory"

Inspired by the mathematical model of integrated pest control,a series of studies on some related problems of biological mathematics were carried out.Starting from actual problems,we have established the"ordinary differential equation model"and the corresponding"periodic impulse control model"respectively;with the rise of the normalized management of integrated pest control and the normalized control of environmental pollution,we established the"state impulse feedback control system"model,referred to as"semi-continuous dynamic system model,put forward the related concept of"semi-continuous dynamic system",created the basic theory,and made a systemic research,for example:the periodic solution of continuous dynamic system and the stability of periodic solutions,homoclinic orbits and homoclinic branches,heteroclinic orbits and heteroclinic branches,and different concepts such as"bilateral control system"and its decision theorem research;the corresponding theory and method of"semi-continuous dynamical system"are further applied to some related problems in other aspects of biomathematics.Based on the mathematical model,this paper summarizes the research process of biomathematics in recent ten years,and points out the problems to be solved in the current research.