一类状态反馈脉冲控制下的营养-产毒浮游植物动力学模型分析

基于生态调水可以改善水环境的实践背景,构建了一类状态反馈脉冲控制下的营养-产毒浮游植物的数学模型.首先研究了无控制系统的有界性、边界平衡点与正平衡点的存在性和稳定性,指出系统可存在一个、两个、三个正平衡点,并证明了鞍结点的存在性.然后利用半连续动力系统理论的后继函数、Bendixson环域定理与压缩映射定理,讨论了系统阶1周期解存在性、唯一性和稳定性.最后,给出数值模拟验证了阶1周期解的存在性.

Dynamical Analysis of a Nutrient-Toxin-Producing Phytoplankton System under State Impulsive Feedback Control

In view of the research on the improvement of water environment by ecological water diversion,a mathematical model of nutrient-toxin-producing phytoplankton under state impulse feedback control is constructed. Firstly,the boundedness,existence and stability of the boundary and positive equilibrium point of the uncontrolled system are investigated. The fact that there maight exist one,two or three positive equilibrium points in the system is pointed out,and the existence of saddle-node point is also proved. Then,the successor function,the Bendixson domain theorem and the contraction mapping principle of semi-continuous dynamical system theory are applied to investigate the existence,uniqueness and stability of order-1 periodic solution. Finally,the existence of order-1 periodic solution is verified by numerical simulation.