一类具有强Allee效应的捕食-食饵模型正平衡态解的存在性  

The existence of positive steady-state solutions of a class predator-prey models with strong Allee effects

作　　者：臧辉[1] 聂华[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2013年第5期5-10,共6页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11001160);教育部"新世纪优秀人才支持计划"(NCET-12-0894)

摘　　要：研究了一类具有强Allee效应的捕食-食饵模型正平衡态解的存在性.以捕食者的增长率d为分歧参数,利用局部分歧理论构造了发自半平凡解的局部分支,并利用全局分歧理论将该局部分支延拓成全局分支,从而得到正平衡态解存在的充分条件.结果表明:当捕食者的增长率d∈(λ1(-mu*2a+u*2),λ1(-mu*1a+u*1)),反映Allee效应强度的参数b∈(0,1/2),且食饵的内禀增长率α>α*时,两者可以共存.The existence of positive solutions of the steady-state system of a predator-prey model with strong Allee effects is discussed. By using local bifurcation theory and regarding the growth rate d of the predator as bifurcation parameter, the local bifurcation branch from the semi-trivial solution branch is investigated, which can be extended to global bifurcation branch by global bifurcation theory. The sufficient conditions for the existence of positive steady-state solutions are gained. It is shown that the model has coexistence solutions whenever the growth rate of the predator d∈ the paramoter b ∈ （0,1/2） which reflects the intensity of strong Allee effect）, and the inherent growth rate of the prey a〉a＊ .

关 键 词：强Allee效应 正解 全局分歧 

分 类 号：O175.25[理学—数学]