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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (4): 84-92.doi: 10.6040/j.issn.1671-9352.0.2023.323

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具有捕食Allee效应和密度依赖扩散的捕食-食饵模型的共存解

马田田,李善兵*   

  1. 西安电子科技大学数学与统计学院, 陕西 西安 710126
  • 出版日期:2025-04-20 发布日期:2025-04-08
  • 通讯作者: 李善兵(1988— ),男,副教授,博士,研究方向为反应扩散方程及其应用. E-mail:lishanbing@xidian.edu.cn
  • 作者简介:马田田(2001— ),女,硕士研究生,研究方向为反应扩散方程及其应用. E-mail:tiantianMA2580@163.com*通信作者:李善兵(1988— ),男,副教授,博士,研究方向为反应扩散方程及其应用. E-mail:lishanbing@xidian.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11901446);中国博士后特别资助项目(2021T140530)

Coexistence solutions of a predator-prey model with Allee effect and density-dependent diffusion in the predator

MA Tiantian, LI Shanbing*   

  1. College of Mathematics and Statistics, Xidian University, Xian 710126, Shaanxi, China
  • Online:2025-04-20 Published:2025-04-08

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摘要： 研究一类齐次Dirichlet边值条件下具有捕食种群Allee效应和密度依赖扩散的捕食-食饵模型的共存解。基于共存解的先验估计,利用正锥上的不动点指数理论建立了共存解存在的充分条件。结果表明,密度依赖扩散对共存解的存在性产生显著影响,同时也发现两物种间的功能反应函数对共存解的存在性有本质的影响。

关键词: 捕食-食饵模型, Allee效应, 密度依赖扩散, 共存解, 不动点指数理论

Abstract: This paper is concerned with the coexistence solutions of a predator-prey model with Allee effect and density-dependent diffusion in the predator under homogeneous Dirichlet boundary conditions. Based on a priori estimate of coexistence solutions, the sufficient conditions for the existence of coexistence solutions are established by using the theory of fixed point index in positive cone. The results show that the density-dependent diffusion has a significant effect on the existence of coexistence solutions, and it is also find that the functional response function between the two species has an essential effect on the existence of coexistence solutions.

Key words: predator-prey model, Allee effect, density-dependent diffusion, coexistence solutions, the theory of fixed point index

中图分类号: 

  • O175
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