Steady-state solutions of a predator-prey model with cross-diffusion and harvesting

LUO Liqin; LI Haixia; WU Shaoyan

doi:10.13471/j.cnki.acta.snus.ZR20240130

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Steady-state solutions of a predator-prey model with cross-diffusion and harvesting

Research articles | 更新时间：2025-11-14

- Steady-state solutions of a predator-prey model with cross-diffusion and harvesting
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 4, Pages: 134-146(2025)
- 作者机构：
  
  宝鸡文理学院数学与信息科学学院，陕西宝鸡 721013
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240130
  CLC： O175.26
- Received：23 April 2024，
  
  Accepted：07 March 2025，
  
  Published Online：27 April 2025，
  
  Published：25 July 2025
- 稿件说明：
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罗丽琴,李海侠,吴绍艳.一类具有交错扩散和捕获项的捕食-食饵模型的稳态解[J].中山大学学报(自然科学版)(中英文),2025,64(04):134-146.

LUO Liqin,LI Haixia,WU Shaoyan.Steady-state solutions of a predator-prey model with cross-diffusion and harvesting[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(04):134-146.
罗丽琴,李海侠,吴绍艳.一类具有交错扩散和捕获项的捕食-食饵模型的稳态解[J].中山大学学报(自然科学版)(中英文),2025,64(04):134-146. DOI： 10.13471/j.cnki.acta.snus.ZR20240130.

LUO Liqin,LI Haixia,WU Shaoyan.Steady-state solutions of a predator-prey model with cross-diffusion and harvesting[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(04):134-146. DOI： 10.13471/j.cnki.acta.snus.ZR20240130.

摘要

研究了一类具有 Crowley-Martin 反应函数和捕获项的捕食-食饵交错扩散模型. 首先，利用线性算子的稳定性理论给出了常数稳态解的稳定条件以及交错扩散驱动的 Turing 不稳定条件. 其次，运用能量估计法和 Leray-Schauder 度理论分别讨论了非常数正稳态解的不存在性和存在性. 最后，通过数值模拟对理论结果进行了验证和补充. 研究结果表明交错扩散对正常数稳态解的稳定性和非常数正稳态解的存在性具有非常重要的影响，会引起模型非均匀空间模式的形成，而且采取合理的捕捞策略能确保种群的可持续发展.

Abstract

A cross-diffusion predator-prey model with Crowley-Martin functional response and harvesting are studied. Firstly， the stable conditions of constant steady-state solutions and the conditions for cross-diffusion-driven Turing instability are obtained by the stability theory of linear operators. Moreover， the nonexistence and existence of non-constant positive steady-state solutions are discussed by using the energy estimation method and Leray-Schauder degree theory. Finally， the theoretical results are varified and supplemented by some numerical simulations. The results indicate that cross-diffusion has very important effects on the stability of constant positive steady-state solution and the existence of non-constant postive steady-state solutions， which can cause the formation of spatial patterns， and reasonable harvesting strategies can ensure the sustainable development of the populations.

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references

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Related Author

LUO Liqin

LI Haixia

GAO Jin

CHENG Shihui

WANG Qiru

DENG Huilin

YAN Xiaoli

QU Chengyuan

Related Institution

．School of Mathematics and Computational Science, Sun Yatsen University

．Department of Information Technology, Henan Institute of Education

Department of Mathematics, Liupanshui Normal College

School of Mathematics and Informatics, Henan Polytechnic University

Department of Mathematics, Dalian Nationalities University

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