Dynamic analysis of a predator-prey system with fear effect and prey refuge

ZHAO Tiantian; HAN Xiaoling

doi:10.11714/acta.snus.ZR20240202

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Dynamic analysis of a predator-prey system with fear effect and prey refuge

Research articles | 更新时间：2026-01-19

- Dynamic analysis of a predator-prey system with fear effect and prey refuge
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 65, Issue 1, Pages: 124-134(2026)
- 作者机构：
  
  西北师范大学数学与统计学院，甘肃兰州 730070
- 作者简介：
- 基金信息：
- DOI：10.11714/acta.snus.ZR20240202
  CLC： O175
- Received：18 June 2024，
  
  Revised：2025-09-30，
  
  Accepted：30 September 2025，
  
  Online First：04 January 2026，
  
  Published：25 January 2026
- 稿件说明：
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赵甜甜,韩晓玲.具有恐惧效应和食饵避难所的捕食者-食饵系统的动力学分析[J].中山大学学报(自然科学版)(中英文),2026,65(01):124-134.

ZHAO Tiantian,HAN Xiaoling.Dynamic analysis of a predator-prey system with fear effect and prey refuge[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(01):124-134.
赵甜甜,韩晓玲.具有恐惧效应和食饵避难所的捕食者-食饵系统的动力学分析[J].中山大学学报(自然科学版)(中英文),2026,65(01):124-134. DOI： 10.11714/acta.snus.ZR20240202.

ZHAO Tiantian,HAN Xiaoling.Dynamic analysis of a predator-prey system with fear effect and prey refuge[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(01):124-134. DOI： 10.11714/acta.snus.ZR20240202.

摘要

提出并研究了一类具有恐惧效应和食饵避难所的捕食者-食饵系统. 首先，证明了系统解的有界性，其次得到了平衡点的存在性和稳定性条件；然后对系统在边界平衡点和内部平衡点处分别发生跨临界分岔和Hopf分岔的条件进行了分析；最后通过数值模拟验证了之前的理论结果.

Abstract

A predator-prey system with fear effect and prey refuge is proposed and studied. First， we prove the boundedness of the solution by comparison principle. Then， we obtain the existence and stability conditions of the equilibrium points. Then， the conditions for the system to undergo transcritical bifurcation and Hopf bifurcation at the boundary equilibrium point and internal equilibrium point are analyzed， respectively. Finally， the previous theoretical results are verified by numerical simulation.

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references

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CHEN Hongbing

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School of Mathematics and Statistics, Tianshui Normal University

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