一类带有时滞效应的修正的Leslie-Gower捕食者–食饵模型动力学分析  

Dynamics Analysis of a Modified Leslie-Gower Predator-Prey Model with Time Delay

作　　者：苏婧婧 

机构地区：[1]温州大学,浙江 温州

出　　处：《应用数学进展》2021年第4期1207-1221,共15页Advances in Applied Mathematics

摘　　要：本文构建了一类带有时滞效应的修正的Leslie-Gower捕食者–食饵模型,旨在研究时滞效应对捕食者–食饵模型动力学性质的影响。运用时滞微分方程理论,分析了模型中由时滞导致的Hopf分岔的存在性。借助于中心流形定理和规范型理论进一步推导Hopf分岔的方向以及周期解的稳定性。此外,数值模拟揭示了种群的密度与平衡点的稳定性对Allee效应、食饵避难以及时滞的变化具有一定的敏感性。This paper constructs a modified Leslie-Gower predator-prey model with Allee effect and prey refuge. The aim of this paper is to study the effect of time delay on the population dynamics. By using delay differential equation theory, we demonstrate the existence of Hopf bifurcation which is induced by time delay. According to center manifold theorem and normal form theory, the direction of Hopf bifurcation and stability of periodic solution are discussed. Additionally, numerical simulations reveal that the population density and the stability of positive equilibrium are sensitive for variations of time delay, Allee effect and prey refuge.

关 键 词：时滞 ALLEE效应 食饵避难 HOPF分岔 

分 类 号：O17[理学—数学]