广西师范大学学报（自然科学版） ›› 2022, Vol. 40 ›› Issue (2): 103-115.doi: 10.16088/j.issn.1001-6600.2021052801

• • 上一篇    下一篇

一类具有迁移和Allee效应的食饵-捕食者系统稳定性

徐王军1, 曹进德2, 伍代勇1, 申传胜1*   

  1. 1.安庆师范大学 数理学院,安徽 安庆 246133;
    2.东南大学 数学学院,江苏 南京 211189
  • 收稿日期:2021-05-02 修回日期:2021-06-28 发布日期:2022-05-31
  • 通讯作者: 申传胜(1975—),男,安徽六安人,安庆师范大学教授,博士。E-mail:csshen@mail.ustc.edu.cn
  • 基金资助:
    国家自然科学基金(11975025);国家自然科学基金委员会与英国皇家学会合作交流项目(12011530158)

Stability of a Prey-predator Model with Migration and Allee Effects

XU Wangjun1, CAO Jinde2, WU Daiyong1, SHEN Chuansheng1*   

  1. 1. School of Mathematics and Physics, Anqing Normal University, Anqing Anhui 246133, China;
    2. School of Mathematics, Southeast University, Nanjing Jiangsu 211189, China
  • Received:2021-05-02 Revised:2021-06-28 Published:2022-05-31

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摘要： 研究一类食饵具有Allee效应且捕食者具有人工控制迁移的食饵-捕食者系统,该系统具有平方根项的功能性反应函数。首先通过定性分析,证明解的有界性,分析平衡点的存在性,得到系统平衡点的局部稳定性的充分条件。接着讨论平衡点的Hopf 分岔存在性,并通过计算第一李雅普诺夫系数,研究平衡点Hopf 分岔的稳定性和方向。 最后通过数值模拟验证所得结论的正确性,结果表明Allee效应和人工控制迁移率对食饵种群和捕食者种群的生存与灭绝具有重要意义。

关键词: 食饵-捕食者模型, Allee效应, 迁移率, Hopf分岔, 稳定性

Abstract: A kind of prey-predator system with Allee effect and artificially controlled migration of predators is studied. The system has a square root functional response function. Firstly, by qualitative analysis of the model, the boundedness of the solution is proved, and the existence of the equilibrium point is analyzed. Sufficient conditions for the local stability of the equilibrium point of the system are obtained. Then, the existence of the Hopf-bifurcation of the equilibrium point is discussed, and the stability and direction of the equilibrium Hopf-bifurcation are studied by calculating the first Lyapunov coefficient. Finally, the correctness of the conclusion is verified by numerical simulation. The results indicate that the Allee effect and artificially controlled migration rate are important for the survival and extinction of prey and predator populations.

Key words: prey-predator model, Allee effect, migration rate, Hopf bifurcation, stability

中图分类号: 

  • Q141
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