一类营养物质-浮游植物mini模型动力学分析  

Dynamical Analyses of Mini Model of Nutrition-Phytoplankton

作　　者：郑亚丽 郭红建 ZHENG Yali;GUO Hongjian(College of Teacher Education,Xinyang Normal University,Xinyang 464000,China;College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院教师教育学院,河南信阳464000 [2]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3期350-355,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371306);信阳师范学院青年科研基金项目(2020-QN-047)。

摘　　要：以富营养化水体中营养物质、生产者和消费者之间的相互作用关系为基础,构建了一类富营养物质-浮游植物的mini模型,并进行定性和稳定性分析.给出了模型的正平衡点个数分别是0、1、2个的充分条件,讨论了相应的稳定性及鞍结点分支,并给出了数值模拟以验证数学结果.模型存在0或1个正平衡点说明,藻类等浮游植物在一定条件下或灭绝或持久生存;模型存在2个正平衡点说明,在不同的初始状态下浮游植物将趋于不同的平衡状态.Based on the interactions relationship among nutrients,producers and consumers in eutrophic water bodies,a mini model of a class of nutrient-phytoplankton was constructed and the qualitative and stability analyses were carried out.The sufficient conditions under which the number of positive equilibrium is 0,1 or 2,respectively,were obtained and the corresponding stability and saddle-node bifurcation were discussed.Numerical simulations were also given to verify the mathematical results.That the model has 0 or 1 positive equilibrium indicates that the phytoplankton such as algae are extinct or persistent under certain conditions;That the model has two positive equilibria indicates that the phytoplankton tends to different equilibrium in different initial state.

关 键 词：富营养物质 浮游植物 平衡点 定性 稳定性 鞍结点分支 

分 类 号：O175.2[理学—数学]