西北师范大学学报（自然科学版）2024，Vol.60Issue(2)：6-13,8.DOI:10.16783/j.cnki.nwnuz.2024.02.002
具有Allee效应和B-D项的Leslie-Gower模型解的存在性
Existence of solutions to Leslie-Gower models with Allee effect and B-D terms
摘要
Abstract
The properties of a class of positive solutions to the improved Leslie-Gower model with B-D reaction terms and Allee effects were studied.Firstly,the maxima principle and the super-sub solution method were used to make a priori estimate for the positive solution of the model,and the asymptotic stability of the normal number solution is obtained by using the linearization operator.Secondly,the Poincare inequality was used to prove the non-existence of non-normal positive solutions.In addition,the Leray-Schauder degree theory was used to clarify the sufficient conditions for the existence of non-constant positive solutions.Finally,numerical simulation was used to verify the stability of the constant solution and the effect of the Allee effect constant on the population density of prey and predator.关键词
Allee效应/渐近稳定性/Leslie-Gower模型/度理论/数值模拟Key words
Allee effect/asymptotic stability/Leslie-Gower model/degree theory/numerical simulation分类
数理科学引用本文复制引用
程丹丹,李畅通,冯孝周,刘梦妍..具有Allee效应和B-D项的Leslie-Gower模型解的存在性[J].西北师范大学学报（自然科学版）,2024,60(2):6-13,8.基金项目
国家自然科学基金资助项目(11901370,12001425) （11901370,12001425）
国家大学生创新创业训练计划项目(202110702010) （202110702010）
陕西省自然科学基础研究计划项目(2020JM-569) （2020JM-569）
西安工业大学研究生教育改革重点项目(XAGDYJ220106) （XAGDYJ220106）
