具时滞和收获的Leslie-Gower种群模型的斑图动力学研究  

Pattern Dynamics Analysis of Leslie-Gower Population Model with Delay and Harvesting

作　　者：常红翠 焦建锋 CHANG Hong-cui;JIAO Jian-feng(School of Economics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China;School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China)

机构地区：[1]郑州航空工业管理学院经济学院,河南郑州450046 [2]郑州航空工业管理学院数学学院,河南郑州450046

出　　处：《数学的实践与认识》2025年第3期146-154,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12401655);河南省自然科学基金(242300421696);河南省高等学校重点科研项目计划基础研究专项(24ZX008,25ZX013)。

摘　　要：在生态环境急剧恶化的背景下,借助经典的捕食模型来研究生物群落的形成、稳定性和相互作用关系等问题,对生态系统的保护、管理和控制等有重要意义.本文主要考虑了一类带有常数时滞和线性收获的反应扩散捕食系统的斑图稳定性分析问题.首先,分析了常微分系统正平衡点的类型及稳定性.随后,研究了对应的时滞微分系统的稳定性,发现当时滞常数小于临界值τ_(0)时,系统渐进稳定,否则,系统将出现Hopf分支.最后,给出了Turing分支存在的参数空间,并分析了收获常数、扩散系数、时滞对Turing失稳现象发生的影响.Under the background of rapidly deteriorating ecological environment,it is of great significance to study the formation,stability,and interaction of biological communities by using classical predator-prey models for the protection,management,and control of ecosystems.This paper mainly considers the problem of pattern stability analysis for a class of reaction-diffusion predator-prey systems with constant delay and linear harvest.Firstly,we analyze the types and stability of positive equilibrium points of ordinary differential systems.Subsequently,we study the stability of the corresponding delay differential system,and find that when the delay constant is less than the critical value To,the system is asymptotically stable,otherwise,the system will undergo Hopf bifurcation.Finally,we give the parameter space where Turing bifurcation exists,and analyze the effects of harvest constant,diffusion coeficient,and delay on the occurrence of Turing instability.

关 键 词：推捕食系统 Turing失稳 时滞 收获 扩散 

分 类 号：O175.1[理学—数学] O175[理学—基础数学]