一类状态脉冲反馈控制下的营养盐–浮游植物动力系统的相关动力学分析

Related Dynamic Analysis of a Nutrient-Phytoplankton Dynamic System under State Impulsive Feedback Control

基于状态脉冲反馈控制理论与非线性动力系统理论,本文在动态建模过程中引入Michaelis-Menten功能反应函数来刻画浮游植物与营养盐的相互作用机制,构建了一类状态脉冲反馈控制下的营养盐–浮游植物动力系统,对所建动力系统进行一些定性分析,建立了该动力系统阶-1周期解的存在性、唯一性和轨道渐近稳定的理论判据,这些研究工作为全面研究状态脉冲反馈控制理论在水体富营养化防治中的应用提供理论支撑。

On the basis of state impulsive feedback control theory and nonlinear dynamic system theory, the Michaelis-Menten functional response function is introduced to describe the interaction mechanism of phytoplankton and nutrients in the process of dynamic modeling;a nutrient-phytoplankton dynamic system under state impulsive feedback control has been structured. Some qualitative analysis of the dynamic system has been investigated to establish some theoretical criterions for the existence, uniqueness and asymptotic stability of the order-1 periodic solution. The research work can provide a theoretical support for the comprehensive study of the application of state impulsive feedback control theory to the prevention and control of eutrophication in water body.