一类捕食-食饵模型正解的惟一性和稳定性  

Uniqueness and stability of positive solutions to a predator-prey model

作　　者：常文丛[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：《纺织高校基础科学学报》2013年第1期43-49,共7页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(11001160);陕西省自然科学基础研究计划项目(2011JQ1015)

摘　　要：考察一类带Beddington-DeAngelis和Leslie反应项的捕食-食饵模型.利用隐函数定理和摄动理论分析了共存解的惟一性和稳定性.结果表明,若假定a≥λ1+a2/k,b>λ1,当参数0<a21,m1,或k1时,模型有惟一正解,且线性稳定.又若当2ka1>ma2时,当参数0<h1时,有相同结论成立.A prey-predator model with Beddington-DeAngelis and Leslie functional response is studied. The uniqueness and stability for the coexistence solutions are given by the implicit function theorem and perturbation technique. It turns out that when a is larger than λ1 ＋a2/k and b is larger than λ1, the uniqueness and stability of positive steady states are obtained with the parameter 0〈a2〈〈1 ,m〉〉1 ,or k〉〉 1. What＇s more,if 2ka1〉ma2 ,the same conclusion is obtained with 0〈h〈〈1.

关 键 词：捕食-食饵模型 隐函数定理 摄动理论 惟一性和稳定性 

分 类 号：O175.26[理学—数学]