在线咨询
中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (2): 220-240.doi: 10.3969/j.issn.1005-3085.2025.02.002

• • 上一篇    下一篇

具有时滞的食饵收获–捕食者转换模型的Hopf分支方向和稳定性

李海荣1,  田艳玲2   

  1. 1. 广州城市理工学院计算机工程学院，广州  510800
    2. 华南师范大学数学科学学院，广州 510631
  • 收稿日期:2022-11-26 接受日期:2023-09-28 出版日期:2025-04-15 发布日期:2025-06-15
  • 通讯作者: 田艳玲 E-mail: tianyl@scnu.edu.cn
  • 基金资助:
    广东省自然科学基金(2020A1515010445)；广州城市理工学院科研项目(56-K0223016; 56-K0223006).

Direction and Stability of the Hopf Bifurcation in a Prey Harvesting and Predator Switching with Time Delay

LI Hairong1,  TIAN Yanling2   

  1. 1. School of Computer Engineering, Guangzhou City University of Technology, Guangzhou 510800
    2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631
  • Received:2022-11-26 Accepted:2023-09-28 Online:2025-04-15 Published:2025-06-15
  • Contact: Y. Tian. E-mail address: tianyl@scnu.edu.cn
  • Supported by:
    The Natural Science Foundation of Guangdong Province (2020A1515010445); the Scientific Research Project of Guangzhou City University of Technology (56-K0223016; 56-K0223006).

摘要：

研究了一类具有时滞的食饵收获与捕食者转换的生态流行病学模型。首先，将系统在正平衡点处线性化，利用特征值法得到一个分支阈值，当捕食者消化时滞超过该阈值时，系统会失稳并出现Hopf分支。其次，基于规范型与中心流形理论，得出了描述系统Hopf分支特征的计算步骤。第三，发现在保持系统的原平衡点不变的情形下，利用线性时滞反馈控制方法可以有效地推迟Hopf分支的发生。最后，进行了数值模拟，以支持分析结果。

关键词: 时滞, Hopf分支, 食饵–捕食者系统, 稳定性, 反馈控制

Abstract:

This study investigates an ecological epidemiological model of prey harvesting and predator switching with time delay. Firstly, the linearization of the system is performed, and the method of analyzing the eigenvalues is used to show that when the predator's digestion delay exceeds a certain bifurcation threshold, the system loses stability and exhibits a Hopf bifurcation. Secondly, based on the theory of normal forms and center manifold, computational steps describing the characteristics of the Hopf bifurcation in the system are derived. Thirdly, under the influence of linear time-delayed feedback control, it is shown that the occurrence of the Hopf bifurcation can be effectively delayed while keeping the original equilibrium point of the system unchanged. Finally, numerical simulations are conducted to support the analytical results.

Key words: delay, Hopf bifurcation, predator-prey system, stability, feedback controller

中图分类号: