基于水生系统的常微分方程平衡点的定性分析  

Qualitative analysis of equilibria of ordinary differential equation based on aquatic system

作　　者：刘煦[1] 陈思潼 LIU Xu;CHEN Si-tong(School of Applied Mathematics,Jilin University of Finance and Economics,Changchun 130117,China;School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]吉林财经大学应用数学学院,吉林长春130117 [2]黑龙江大学数学科学学院,黑龙江哈尔滨150080

出　　处：《东北师大学报（自然科学版）》2022年第2期36-42,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11701209);吉林财经大学科学研究重点资助项目(2018Z02)。

摘　　要：针对一类常微分方程的平衡点进行定性分析,探讨了该类方程边界平衡点及正平衡点的存在性、唯一性及稳定性,并利用数值模拟,验证了所得理论结果的有效性.The equilibria of a class of ordinary differential equations is qualitatively analyzed, which describes a class of shallow water eco system.The existence, uniqueness and stability of boundary equilibrium and positive equilibrium of the equation are discussed, and the validity of the theoretical results are verified by numerical simulation.

关 键 词：平衡点 局部渐近稳定性 阈值条件 

分 类 号：O29[理学—应用数学]