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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (10): 43-53.doi: 10.6040/j.issn.1671-9352.0.2022.308

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含有猎物避难所和恐惧效应的反应扩散捕食者-食饵模型的动力学

曹倩1(),李艳玲2,*(),单炜华1   

  1. 1. 长安大学理学院, 陕西 西安 710064
    2. 陕西师范大学数学与统计学院, 陕西 西安 710119
  • 收稿日期:2022-05-30 出版日期:2023-10-20 发布日期:2023-10-17
  • 通讯作者: 李艳玲 E-mail:mathcq19@chd.edu.cn;yanlingl@snnu.edu.cn
  • 作者简介:曹倩(1989—)，女，讲师，博士研究生，研究方向为反应扩散方程和生物数学. E-mail: mathcq19@chd.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12101075);国家自然科学基金资助项目(61872227);陕西省自然科学基础研究计划资助项目(2021JQ-217);陕西省自然科学基础研究计划资助项目(2022JQ-054);中央高校基本科研业务费专项资金资助项目(300102122114)

Dynamics of a reaction-diffusion predator-prey model incorporating prey refuge and fear effect

Qian CAO1(),Yanling LI2,*(),Weihua SHAN1   

  1. 1. School of Science, Chang'an University Xi'an 710064, Shaanxi, China
    2. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, Shaanxi, China
  • Received:2022-05-30 Online:2023-10-20 Published:2023-10-17
  • Contact: Yanling LI E-mail:mathcq19@chd.edu.cn;yanlingl@snnu.edu.cn

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摘要：

针对具有猎物避难所和恐惧效应的反应扩散捕食者-食饵系统, 研究系统正常数解的图灵不稳和系统解的先验估计, 并证明在一定的参数条件下系统非常数正稳态解的不存在性。此外, 以捕食者的扩散系数为分歧参数, 构建分歧解的全局结构, 得到当捕食者的扩散系数大于某个临界值时, 分歧解可以延拓到无穷。最后, 通过数值模拟验证并补充理论结果。

关键词: 图灵不稳, 分歧理论, 猎物避难所, 恐惧效应, 反应扩散捕食者-食饵模型

Abstract:

For a reaction-diffusion predator-prey system with prey refuge and fear effect, the Turing instability of the positive constant solution for the system and a priori estimates of solutions for the system are investigated. It is proved that there is no nonconstant positive steady-state solution for the system under certain parameter conditions. Moreover, taking the diffusion coefficient of the predator as the bifurcation parameter, the global structure of the bifurcation solution is constructed. It is found that the bifurcation solution can be extended to infinity when the diffusion coefficient of predator is greater than some critical value. Finally, by numerical simulations, the theoretical results are verified and supplemented.

Key words: Turing instability, bifurcation theory, prey refuge, fear effect, reaction-diffusion predator-prey model

中图分类号: 

  • O175

图1

当$d_{2}=1<\tilde{d}_{2}$时系统(1)产生的时空模式"

图2

当$d_{2}=500>\tilde{d}_{2}$时系统(1)产生的时空模式"

图3

当d1=0.1时系统(1)产生的时空模式"

图4

当m=0时系统(1)产生的时空模式"

图5

当k=0、d1=0.01和d2=500时系统(1)产生的时空模式"

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