山西大学学报（自然科学版）2025，Vol.48Issue(4)：677-691,15.DOI:10.13451/j.sxu.ns.2024011
具有时滞的Holling-Ⅲ型捕食系统的Hopf分支
Hopf Bifurcation in a Holling-Ⅲ Predator System with Time Delay
摘要
Abstract
In this paper,a Holling-Ⅲ predator-prey system with time delay under the homogeneous Neumann boundary conditions is studied.Firstly,by choosing the time delay as the bifurcation parameter,we study the effect of time delay on the stability of the posi-tive equilibrium point of the system,thereby the conditions for generating Hopf bifurcations are obtained.Secondly,with the aid of partial functional differential equations of center manifold theory and standard method,the direction of the Hopf bifurcations and sta-bility of periodic solutions of a bifurcation are gained.Finally,by using the numerical simulation function of MATLAB software,the theoretical results proposed in the paper are tested.关键词
时滞/存在性/稳定性/数值模拟Key words
time delay/existence/stability/numerical simulation分类
数理科学引用本文复制引用
张嘉祥,袁海龙,樊雨..具有时滞的Holling-Ⅲ型捕食系统的Hopf分支[J].山西大学学报（自然科学版）,2025,48(4):677-691,15.基金项目
国家自然科学基金(11901370) （11901370）
陕西省自然科学基础研究计划(2019JQ-516) （2019JQ-516）
陕西省教育厅专项科研计划(19JK0142) （19JK0142）
陕西省科协人才托举项目(20200508) （20200508）
国家博士后基金(2019M653578) （2019M653578）
