浙江大学学报（理学版）2025，Vol.52Issue(6)：690-698,705,10.DOI:10.3785/j.issn.1008-9497.2025.06.003
一类具有Allee效应和恐惧效应的Leslie-Gower捕食者-食饵扩散模型的动力学分析
Dynamic analysis of a diffusive Leslie-Gower predator-prey model with Allee effect and fear effect
摘要
Abstract
A diffusive Leslie-Gower predator-prey model with Allee effect on prey and fear effect on predator is studied.Firstly,the global existence,uniqueness and dissipation of positive solutions are discussed by virtue of the comparison principle of parabolic systems.Secondly,the stability of constant steady-state solutions is analyzed by means of the eigenvalue theory of linear operators.Finally,the nonexistence and existence of non-constant positive steady-state solutions are investigated by means of the combination of the energy estimation method and Leray-Schauder degree theory.The results demonstrate that when the Allee effect and diffusion rate of the prey are moderate and the diffusion rate of the predator is sufficiently large,the fear effect on the predator can effectively lead to coexisting of both prey and predator.关键词
Leslie-Gower捕食者-食饵模型/Allee效应/恐惧效应/稳定性/Leray-Schauder度理论Key words
Leslie-Gower predator-prey model/Allee effect/fear effect/stability/Leray-Schauder degree theory分类
数理科学引用本文复制引用
李海侠,路银豆,罗丽琴..一类具有Allee效应和恐惧效应的Leslie-Gower捕食者-食饵扩散模型的动力学分析[J].浙江大学学报（理学版）,2025,52(6):690-698,705,10.基金项目
国家自然科学基金资助项目(12271431) （12271431）
陕西省科技厅工业攻关项目(2022GY-071). （2022GY-071）
