一类具有物质循环和状态反馈控制的营养-浮游植物模型研究  

Studies on a Nutrient-phytoplankton Model with Nutrient Cycle and State Feedback Control

作　　者：郭红建 吴春鹤 GUO Hongjian;WU Chunhe(College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2021年第4期524-530,共7页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671346,11371306);信阳师范学院研究生科研创新基金项目(2020KYJJ30)。

摘　　要：基于控制水体水质的实践,以恒化器模型为基础,构建了一类具有物质循环和状态反馈控制的营养-浮游植物模型.首先研究了连续模型的定性与稳定性性质,给出了平衡点存在性及稳定性的条件;然后利用半连续动力系统的理论及后继函数等方法,证明了在一定条件下状态反馈控制模型存在唯一轨道渐近稳定的周期解.数值模拟验证了理论结果.这些数学结果表明:在状态反馈控制下藻类等浮游植物可以被控制在给定阈值以下.Based on the practice of controlling water quality,a kind of nutrition-phytoplankton model with nutrient cycle and state feedback control was established on the basis of the chemostat model.Firstly,the qualitative and stability of the continuous model were studied,and the conditions for the existence and stability of equilibria were given.Then,by using the theory of semi-continuous dynamical system and the method of successor function,the conditions under which the model has an unique and asymptotically stable periodic solution were obtained.Numerical simulations verified the theoretical results.The results showed that the phytoplankton such as algae can be controlled below the given threshold under the state feedback control.

关 键 词：状态反馈控制 物质循环 后继函数 营养-浮游植物模型 

分 类 号：O175.2[理学—数学]