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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (4): 72-83.doi: 10.6040/j.issn.1671-9352.0.2023.338

• • 上一篇    

具有非局部竞争和时滞的广食性捕食者-食饵模型的Hopf分支

罗艺华,杜燕飞*   

  1. 陕西科技大学数学与数据科学学院, 陕西 西安 710021
  • 发布日期:2025-04-08
  • 通讯作者: 杜燕飞(1984— ),女,副教授,硕士生导师,博士,研究方向为微分方程与动力系统、分支理论. E-mail:duyanfei@sust.edu.cn
  • 作者简介:罗艺华(2000— ),女,硕士研究生,研究方向为反应扩散方程的分支理论. E-mail:1561227763@qq.com*通信作者:杜燕飞(1984— ),女,副教授,硕士生导师,博士,研究方向为微分方程与动力系统、分支理论. E-mail:duyanfei@sust.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11901369);陕西科技大学博士启动资金资助项目(2023BJ-13)

Hopf bifurcation in a diffusive generalist predator-prey system with nonlocal competition and time delay

LUO Yihua, DU Yanfei*   

  1. School of Mathematics &
    Data Science, Shaanxi University of Science &
    Technology, Xian 710021, Shaanxi, China
  • Published:2025-04-08

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摘要： 利用特征方程根的分布分析方法,研究了正平衡点的稳定性和Hopf分支的存在性,得到了系统在发生Hopf分支时的时滞临界值。利用中心流形定理和规范型理论,确定了分支方向和分支周期解的稳定性。系统可能存在无食饵边界平衡点与正平衡点双稳、无食饵边界平衡点与周期解双稳2种双稳态,通过数值模拟验证了理论结果。

关键词: 广食性捕食者, 非局部竞争, 时滞, Hopf分支, 双稳

Abstract: The stability of positive equilibrium and the existence of Hopf bifurcation are studied by analyzing the distribution of eigenvalues. The critical time delay of Hopf bifurcation is obtained. Applying center manifold method and normal form theory, the direction of Hopf bifurcation and stability of the bifurcating periodic solution are discussed. It is shown that there are two types of bistability. The prey-free equilibrium and the positive equilibrium are both stable. The prey-free equilibrium and the periodic solution are both stable. Numerical simulations are presented to support the theoretical results.

Key words: generalist predator, nonlocal competition, time delay, Hopf bifurcation, bistability

中图分类号: 

  • O175
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