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

作　　者：程丹丹 李畅通 冯孝周[1] 刘梦妍 CHENG Dan-dan;LI Chang-tong;FENG Xiao-zhou;LIU Meng-yan(School of Science,Xi an Technological University,Xi an 710021,Shaanxi,China)

机构地区：[1]西安工业大学基础学院,陕西西安710021

出　　处：《西北师范大学学报（自然科学版）》2024年第2期6-13,共8页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11901370,12001425);国家大学生创新创业训练计划项目(202110702010);陕西省自然科学基础研究计划项目(2020JM-569);西安工业大学研究生教育改革重点项目(XAGDYJ220106)。

摘　　要：研究一类具有B-D反应项和Allee效应的改进Leslie-Gower模型正解的性质.首先,运用极大值原理、上下解方法对模型正解进行先验估计,利用线性化算子得到正常数解的渐近稳定性.其次,利用Poincare不等式证明非常数正解的不存在性,进一步,利用Leray-Schauder度理论阐明非常数正解存在的充分条件.最后,通过数值模拟验证常数解的稳定性及Allee效应常数对食饵和捕食者种群密度的影响.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 

分 类 号：O175.25[理学—数学]