一类生态调水策略下的营养-浮游植物Filippov模型的动力学分析  

Dynamic Analysis of Filippov Model for a Kind of Nutrition-Phytoplankton Based on Ecological Water Diversion

作　　者：郭红建 朱聪聪 GUO Hongjian;ZHU Congcong(College of Mathematics and Information Sciences,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院数学与统计学院

出　　处：《信阳师范学院学报（自然科学版）》2019年第4期517-524,共8页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371306);信阳师范学院研究生科研创新基金项目(2018KYJJ39)

摘　　要：基于生态调水可以改善水环境的实践背景,构建了一类营养-浮游植物的Fillipov动力学模型.首先研究了子系统的定性和稳定性,指出子系统分别存在一个全局稳定的正平衡点.然后讨论了Fillipov模型的滑模动力学性质,包括实平衡点、虚平衡点、伪平衡点和切点的存在性和稳定性.最后,理论分析和数值模拟给出了与边界平衡点有关的滑动分支,并讨论了相应的生态学意义.Based on the practical background that ecological water diversion can improve water environment,a Filippov dynamic model of nutrient phytoplankton is constructed.Firstly,the qualitative properties and stability of the subsystems are studied.It is pointed out that the subsystems may have a globally stable positive equilibrium point,respectively.Secondly,the sliding mode dynamics of the Filippov system,including the existence and stability of the real equilibrium point,the virtual equilibrium point,the pseudo equilibrium point and the tangent point,are discussed.Finally,the sliding bifurcations related to the boundary equilibrium point are given by theoretical analysis and numerical simulation,and the corresponding biological significance is given.

关 键 词：水体富营养化 生态调水 Filippov模型 滑模动力学 

分 类 号：O175.5[理学—数学]