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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (4): 104-117.doi: 10.6040/j.issn.1671-9352.0.2023.511

• • 上一篇    

一类具有合作捕获与群体防御的扩散捕食者-食饵模型的动力学分析

徐英婷,赵建涛,魏新*   

  1. 黑龙江大学数学科学学院, 黑龙江 哈尔滨 150080
  • 发布日期:2025-04-08
  • 通讯作者: 魏新(1982— ),女,副教授,博士,研究方向为微分方程分支理论的研究及应用. E-mail:weixin@hlju.edu.cn
  • 作者简介:徐英婷(1999— ),女,硕士研究生,研究方向为微分方程分支理论的研究及应用. E-mail:xyingt1999@163.com*通信作者:魏新(1982— ),女,副教授,博士,研究方向为微分方程分支理论的研究及应用. E-mail:weixin@hlju.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11901172);黑龙江省省属高校基本科研业务费(2022-KYYWF-1043,2021-KYYWF-0017)

Dynamical analysis in a diffusive predator-prey model with cooperative hunting and group defense

XU Yingting, ZHAO Jiantao, WEI Xin*   

  1. School of Mathematical Science, Heilongjiang University, Harbin 150080, Heilongjiang, China
  • Published:2025-04-08

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摘要： 建立具有扩散、合作捕获和群体防御的捕食者-食饵模型,并研究扩散引起的Turing不稳定性以及Turing-Hopf分支的存在性。以扩散作为分支参数,分析该模型共存稳态解的稳定性,通过计算Turing-Hopf分支点附近的规范型,深入探讨系统的复杂动力学性质。此外,通过数值模拟对理论分析的结果进行解释。研究结果表明,系统在Turing-Hopf分支点附近展现出复杂的动力学行为,包括稳态解、齐次周期解、非齐次稳态解和非齐次周期解等。

关键词: 合作捕获, 群体防御, Turing-Hopf分支, 扩散, 捕食者-食饵模型

Abstract: In this paper, we propose a diffusive predator-prey model with cooperative hunting and group defense, and investigate the existence of Turing instability and Turing-Hopf bifurcation induced by diffusion. Taking coefficient of diffusion as bifurcation parameter, we analyze the stability of the coexistence equilibrium, and explore the complex dynamical behaviours of the system by calculating the normal forms near the Turing-Hopf bifurcation points. Moreover, we carry out some numerical simulations to illustrate the theoretical analysis. Our study shows that the system demonstrates complex dynamical behaviours near the Turing-Hopf bifurcation point, including steady-state solutions, homogeneous periodic solutions, non-homogeneous steady-state solutions, and non-homogeneous periodic solutions.

Key words: cooperative hunting, group defense, Turing-Hopf bifurcation, diffusion, predator-prey model

中图分类号: 

  • O175
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