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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 ›› 2026, Vol. 43 ›› Issue (1): 90-102.doi: 10.3969/j.issn.1005-3085.2026.01.006cstr: 32411.14.cjem.CN61-1269/O1.2026.01.006

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具有时滞的Leslie-Gower互惠捕获系统的动力学分析

殷溪曼,  孙  悦,  江 娇   

  1. 上海海事大学理学院，上海 201306
  • 收稿日期:2023-04-29 接受日期:2024-04-14 出版日期:2026-02-15 发布日期:2026-04-15
  • 通讯作者: 江娇 E-mail: jiaojiang@shmtu.edu.cn
  • 基金资助:
    国家自然科学基金 (12271346).

The Dynamics of a Leslie-Gower Model with Delay and Hunting Cooperation

YIN Ximan,  SUN Yue,  JIANG Jiao   

  1. School of Science, Shanghai Maritime University, Shanghai 201306
  • Received:2023-04-29 Accepted:2024-04-14 Online:2026-02-15 Published:2026-04-15
  • Contact: J. Jiang. E-mail address: jiaojiang@shmtu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (12271346).

摘要：

主要研究了具有孕育时滞和互惠捕获的捕食–食饵系统的正平衡态的稳定性及Hopf分支。首先，分析了没有时滞的Leslie-Gower互惠捕获系统解的正性、有界性及正平衡态的存在性、全局稳定性。其次，讨论了食饵孕育时滞对模型动力学的影响：时滞会使系统产生单个或多个稳定性开关，并诱发Hopf分支的发生。最后，在不同时滞下做数值模拟，进一步检验了前面的分析结果。

关键词: 捕食–食饵模型, Leslie-Gower, 互惠捕获, 稳定性, Hopf分支, 时滞

Abstract:

In this paper, the stability and Hopf bifurcation of the positive equilibrium in a predator-prey system with gestation delay and hunting cooperation are studied. Firstly, we analyze the positivity and boundedness of the general solutions with initial conditions of the system without time delay, prove the existence and global stability of the positive equilibrium. Secondly, the effects of gestation delay on the model dynamics are discussed. When the time delay increases to a certain critical value, the stability of the positive equilibrium changes with a single stability switch or multiple stability switches, and the Hopf bifurcation can occur. Fina-lly, numerical simulation with different time delays is carried out to further verify the above analysis results.

Key words: predator-prey model, Leslie-Gower, hunting cooperation, stability, Hopf bifurcation, time delay

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