时滞湖泊生态模型的稳定性与Hopf分支  

Stability and Hopf Bifurcation of Lake Ecological Model with Time Delay

作　　者：张二丽[1] 邢玉清 ZHANG Er-li;XING Yu-qing(School of Information Engineering,Zhengzhou Institute of Finance and Economics,Zhengzhou 450044,China;Information Engineering University,Zhengzhou 450001,China;College of Sciences,Henan Agricultural University,Zhengzhou 450002,China)

机构地区：[1]郑州财经学院信息工程学院,河南郑州450044 [2]信息工程大学网络空间安全学院,河南郑州450001 [3]河南农业大学理学院,河南郑州450002

出　　处：《数学的实践与认识》2020年第15期314-320,共7页Mathematics in Practice and Theory

基　　金：河南省高等学校青年骨干教师培养计划项目(2017GGJS202);河南省高等学校重点科研项目(19A110033);河南农业大学创新基金(KJCX2017A19)。

摘　　要：研究了具有时滞的外来有机物-浮游植物-浮游动物湖泊生态模型.通过研究该模型在平衡点处的特征方程,得到了使平衡点稳定的时滞的取值范围.并且发现当时滞取某些特定值时,在平衡点附近会出现周期解.与已有的研究结果相比较发现,时滞对湖泊生态系统的稳定性有着重要的影响.最后,我们给出一个数值算例来验证理论结果.In this paper,cross ecosystem resources-phytoplankton-zooplankton model is studied.By analyzing the corresponding characteristic equation,the range of time delay which makes the equilibrium point stable is obtained.When the time delay takes some specific values periodic solutions will appear near the equilibrium point.Compared with the existing results,it is found that the time delay has an important influence on the stability of the lake ecosystem.Finally,we give a numerical example to verify the theoretical results.

关 键 词：时滞 稳定性 HOPF分支 

分 类 号：O175[理学—数学] Q178[理学—基础数学]