基于微分方程定性理论的一类修正时滞Leslie-Gower模型动力学分析  

Dynamic Analysis of a Modified Leslie-Gower Model with Time Delay Based on Qualitative Theory of Differential Equations

作　　者：李顺杰[1] 江文静 张学兵 LI Shun-jie;JIANG Wen-jing;ZHANG Xue-bing(College of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《数学的实践与认识》2023年第9期201-207,共7页Mathematics in Practice and Theory

基　　金：江苏省高等教育教改研究立项课题(2021JSJG335);高等学校大学数学教学研究与发展中心教改项目(CMC20210304);江苏省高等教育学会“大学生劳动教育”“基础课课程群”专项重点课题(2021JDKT006);国家自然科学基金(11801280)。

摘　　要：考虑环境密度制约延迟因素,建立了一个修正的时滞Leslie-Gower捕食模型.然后,利用微分方程定性理论,研究新模型的平衡点及稳定性,并以时滞为分岔参数,研究模型Hopf分支的存在性.最后,利用Matlab软件进行数值仿真,结果表明时滞会导致平衡点失去稳定性并产生Hopf分支,当时滞增大时系统甚至会出现混沌现象.This paper establishes a modified Leslie-Gower model by incorporating the time delay into the resource limitation of the prey logistic equation.Then,the equilibrium points and their stability are analyzed by the qualitative theory of differential equations.The Hopf bifurcation induced by the time delay variable is also investigated.Finally,numerical simulations show that the time delay will lead to the instability of the equilibrium points and Hopf bifurcation.Moreover,the chaos behavior could even occur when time delay increases.

关 键 词：Leslie-Gower模型 时滞 稳定性 HOPF分支 

分 类 号：O175[理学—数学]