数学季刊 ›› 2024, Vol. 39 ›› Issue (2): 128-143.doi: 10.13371/j.cnki.chin.q.j.m.2024.02.002

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具有食饵避难所的离散捕食者-食饵模型的余维二分支分析

庞茹一, 陈巧玲   

  1. College of Science, Xi’an Polytechnic University, Xi’an 710600, China
  • 收稿日期:2023-07-14 出版日期:2024-06-30 发布日期:2024-06-30
  • 通讯作者: CHEN Qiao-ling (1987-), female, native of Xi’an, Shaanxi, professor of Xi’an Polytechnic University, engages in biomathematics. E-mail: chenqiaoling@xpu.edu.cn
  • 作者简介:PANG Ru-yi (1998-), female, native of Zhoukou, Henan, graduate student of Xi’an Polytechnic University, engages in biomathematics; CHEN Qiao-ling (1987-), female, native of Xi’an, Shaanxi, professor of Xi’an Polytechnic University, engages in biomathematics.
  • 基金资助:
    Supported by the National Natural Science Foundation of China (Grant No. 12271421); The Shaanxi Province Innovation Talent Promotion Plan Project (Grant No. 2023KJXX-056).

Codimension-Two Bifurcations Analysis of a Discrete Predator-Prey Model Incorporating a Prey Refuge

PANG Ru-yi, CHEN Qiao-ling   

  1. College of Science, Xi’an Polytechnic University, Xi’an 710600, China
  • Received:2023-07-14 Online:2024-06-30 Published:2024-06-30
  • Contact: CHEN Qiao-ling (1987-), female, native of Xi’an, Shaanxi, professor of Xi’an Polytechnic University, engages in biomathematics. E-mail: chenqiaoling@xpu.edu.cn
  • About author:PANG Ru-yi (1998-), female, native of Zhoukou, Henan, graduate student of Xi’an Polytechnic University, engages in biomathematics; CHEN Qiao-ling (1987-), female, native of Xi’an, Shaanxi, professor of Xi’an Polytechnic University, engages in biomathematics.
  • Supported by:
    Supported by the National Natural Science Foundation of China (Grant No. 12271421); The Shaanxi Province Innovation Talent Promotion Plan Project (Grant No. 2023KJXX-056).

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摘要：  In this paper, a discrete predator-prey model with prey refuge is investigated. It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances. The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors, such as limit cycle, periodic solutions, chaos and codimension-1 bifurcations.

关键词:  Refuge, Discrete predator-prey model, Codimension-2 bifurcations, Chaos

Abstract:  In this paper, a discrete predator-prey model with prey refuge is investigated. It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances. The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors, such as limit cycle, periodic solutions, chaos and codimension-1 bifurcations.

Key words:  Refuge, Discrete predator-prey model, Codimension-2 bifurcations, Chaos

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