正比例收获滞后Logistic单种群模型的稳定性分析  

Stability Analysis of Time Delay Logistic Single Population Growth Model with Direct Proportional Harvest

作　　者：叶陆红 YE Luhong(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2022年第1期79-81,共3页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安庆师范大学校级教研项目(2019aqnujyxm61);安徽省高等学校省级质量工程项目(2020jxtd156)。

摘　　要：稳定性是生态系统中最基本的特征之一,也是不受干涉地保持不变的能力。在微分方程的研究中,稳定性意味着初始状态下的小扰动不会引起解的大的变化。在单组模型中比较经典的是Logistic模型,但是许多研究忽略了未知函数和过去时间之间的关系,因此研究滞后单种群生长模型的稳定性具有重要的现实意义。本文主要针对正比例收获的滞后Logistic单种群生长模型,采用τ划分特征根分析法,得到时滞在不同条件下,模型的正平衡解渐近稳定、不稳定及出现Hopf分支的结论,体现时滞对平衡点的稳定性影响。并通过数值模型验证了正平衡解渐近稳定的结论。Stability is one of the most fundamental characteristics of the ecosystem.It is the ability to remain unchanged without interference.In the study of differential equations,stability means that small perturbations in the initial state will not lead to large changes in the solution.In the single population model,the classic one is Logistic model,while many studies ignore the relationships between unknown functions and the past time,namely time delay.Therefore,it is of great practical significance to study the stability of single population growth model with time delay.In this paper,we study the delayed Logistic single population growth model with direct proportion harvest.By dividing characteristic root analysis,we get the conclusion that the positive equilibrium solution of the model is asymptotically stable,unstable and Hopf bifurcation occurs under different conditions with parameter delay.That is the influence of time delay on the stability of the equilibrium point.The conclusion that the positive equilibrium solution of the model is asymptotically stable is verified by numerical model.

关 键 词：正比例收获 时滞 τ划分 稳定性 

分 类 号：O175[理学—数学]