具有群体性行为的捕食者-食饵系统稳定性分析  

Stability Analysis of a Predator-Prey System with Group Behavior

作　　者：李梦婷 周文 LI Mengting;ZHOUWen*(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《安庆师范大学学报（自然科学版）》2023年第2期103-109,共7页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11671013);安徽省自然科学基金(2008085MA13)。

摘　　要：本文研究了具有时滞和平方根功能反应函数的反应扩散捕食者-食饵系统动力学特性。首先研究了系统正平衡点的存在性,其次通过稳定性分析和Hopf分支分析获得了产生Hopf分支的条件,结果说明时滞对系统的Hopf分支存在影响。最后通过数值模拟验证了相关理论,结果发现具有群体性行为的捕食者-食饵系统拥有丰富的动力学行为。In this work,a diffusive predator-prey model with square root functional response and delay has been investi-gated.We analyze the existence of a positive constant steady state.Then the conditions for occurrence of Hopf bifurcation are obtained through linear stability analysis and Hopf bifurcation analysis.The results show that delay has impact on the occur-rence of Hopf bifurcation.Finally,numerical simulations are carried out to verify the correctness of our theory.The conclu-sions show that the predator-prey system with group behavior has rich dynamic behavior.

关 键 词：捕食者-食饵系统 HOPF分支 稳定性分析 时滞 扩散 

分 类 号：O175.2[理学—数学] O193[理学—基础数学]