中山大学学报（自然科学版）（中英文）2025，Vol.64Issue(4)：134-146,13.DOI:10.13471/j.cnki.acta.snus.ZR20240130
一类具有交错扩散和捕获项的捕食-食饵模型的稳态解
Steady-state solutions of a predator-prey model with cross-diffusion and harvesting
摘要
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.关键词
捕食-食饵交错扩散模型/Crowley-Martin反应函数/捕获项/Turing不稳定/存在性Key words
cross-diffusion prepator-prey model/Crowley-Martin functional response/harvesting/Turing instability/existence分类
数理科学引用本文复制引用
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(4):134-146,13.基金项目
国家自然科学基金(12271431,12061081) （12271431,12061081）
陕西省科技厅工业公关项目(2022GY-071) （2022GY-071）
