Qualitative Analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect  

具有非局部恐惧效应的捕食者食饵模型的动力学分析

作　　者：Shen Zhongyuan Zhang Xuebing Li Shunjie 沈中原;张学兵;李顺杰(南京信息工程大学数学与统计学院,南京210044;南京信息工程大学江苏省应用数学中心,南京信息工程大学江苏省系统建模与数据分析国际合作联合实验室,南京210044)

机构地区：[1]School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China;[2]Center for Applied Mathematics of Jiangsu Province,Jiangsu International Joint Laboratory on System Modeling and Data Analysis,Nanjing 210044,China

出　　处：《数学理论与应用》2024年第3期67-82,共16页Mathematical Theory and Applications

基　　金：supported by the National Natural Science Foundation of China (No.12271261);the National Undergraduate Training Program for Innovation and Entrepreneurship (No.202310300044Z)。

摘　　要：In this paper,we establish a delayed predator-prey model with nonlocal fear effect.Firstly,the existence,uniqueness,and persistence of solutions of the model are studied.Then,the local stability,Turing bifurcation,and Hopf bifurcation of the constant equilibrium state are analyzed by examining the characteristic equation.The global asymptotic stability of the positive equilibrium point is investigated using the Lyapunov function method.Finally,the correctness of the theoretical analysis results is verified through numerical simulations.本文建立一个具有非局部恐惧效应的时滞捕食者食饵模型,首先研究模型解的存在性、有解性以及持久性.接着通过分析其特征方程,研究其常数平衡态的局部稳定性、Turing分支以及Hopf分支?利用Lypunov函数方法研究其正平衡点的全局渐近稳定性.最后,利用数值仿真验证理论分析结果的正确性.

关 键 词：Delay Nonlocal fear effect Global stability Hopf bifurcation 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]