具有弱Allee效应的三斑块捕食-食饵扩散模型动力学分析  

Dynamic Analysis of Three-Patch Predator-Prey Diffusion Model with Weak Allee Effect

作　　者：朱兆镭 杨志春 周伟松 ZHU Zhaolei;YANG Zhichun;ZHOU Weisong(School of Science,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆邮电大学理学院,重庆400065 [2]重庆师范大学数学科学学院,重庆401331

出　　处：《应用数学》2024年第4期952-961,共10页Mathematica Applicata

基　　金：国家自然科学基金面上项目(11971081);重庆英才创新领军人才计划项目(cstc2024ycjh-bgzxm0046);重庆师范大学数学学院开放课题项目(CSSXKFKTM202007);重庆市科委一般项目(cstc2020jcyj-msxmX0593,cstc2019jcyj-msxmX0716);重庆市教委项目(KJQN202000601,KJQN201900619)。

摘　　要：本文建立一类具有弱Allee效应的三斑块捕食-食饵扩散模型,并研究食饵的Allee效应和食饵的扩散对模型正平衡点的存在性及稳定性的影响.首先,分析了模型永久持续生存的充分条件.其次,利用图理论构造出新的Lyapunov函数,得到模型正平衡点是全局渐近稳定的充分条件.最后利用Matlab软件对分析结果进行数值验证.A three-patch predator-prey diffusion model with the weak Allee effect is established.And the Allee effect of prey and the influence of prey diffusion on the existence and stability of the positive equilibrium point of the model are studied.Firstly,the sufficient condition for the model to permanence is analyzed.Secondly,a new Lyapunov function is constructed by applying graph theory,and the positive equilibrium point of the model is a sufficient condition for global asymptotic stability.Finally,Matlab software is used to verify the analysis results.

关 键 词：捕食-食饵模型 斑块 ALLEE效应 永久持续生存 全局渐近稳定 

分 类 号：O175.13[理学—数学]