具有非局部恐惧效应的捕食模型的分支研究  

Bifurcation Analysis of a General Predator-prey Model with Nonlocal Fear Effect

作　　者：孙秀丽 Xiuli Sun(School of Mathematics,Taiyuan University of Technology,Jinzhong 030600,P.R.China)

机构地区：[1]太原理工大学数学学院,晋中030600

出　　处：《数学学报(中文版)》2025年第1期56-66,共11页Acta Mathematica Sinica:Chinese Series

基　　金：2021年山西省基础研究计划项目(20210302124379)。

摘　　要：已有大量证据表明,捕食者引起的恐惧效应可以对食饵产生间接影响,其效果可与直接捕杀食饵相媲美.本文构建了一个具有非局部恐惧效应的扩散型捕食系统,并对其进行了深入研究.首先考察了系统解的存在性和有界性,随后讨论了常数稳态解的稳定性,并通过采用Lyapunov-Schmidt方法详细研究了稳态分支现象,最后利用数值模拟验证了理论结果的正确性.It has been well established that the predator-induced fear has indirect impact on prey but can have comparable effects on prey population as direct killing.In this paper,a diffusive predator-prey system with nonlocal fear effect is formulated and investigated.We firstly study the existence and boundedness of solutions and then discuss the stability of constant steady states.Steady-state bifurcations are carried out in detail by using the Lyapunov—Schmidt method.Finally,numerical simulations are showed to verify our theoretical results.

关 键 词：捕食模型 非局部恐惧效应 稳定性 稳态分支 

分 类 号：O175.2[理学—数学]