一类捕食-食饵模型共存解的存在性与稳定性  

Coexistence of existence and stability of a predator-prey model

作　　者：袁海龙[1] 李艳玲[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）》2014年第1期15-18,共4页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11271236);教育部高等学校博士学科点专项科研基金项目(200807180004)

摘　　要：研究了一类具有HollingⅢ型捕食-食饵模型平衡态正解的存在性与稳定性.利用锥上的不动点理论给出正解存在的充分条件;讨论了m充分大时,借助上下解方法构造出模型的正解,并根据线性稳定性理论讨论了该正解的稳定性.结果表明:当参数a>λ1,c>λ1(-dθ2a/(1+mθ2a))时,共存解存在,且当c>λ1时,共存解是线性稳定的.Abstract： The existence and stability of positive solutions are investigated for a predator-prey model with Holling type [[[ functional response. By using the fixed point index in cones, one can reduce the sufficient conditions for any possible positive solutions. When m is suitably large,by the super-sub solution method for predator-prey systems, the positive solutions and the stability of the positive solutions are studied by using the linearized stability. It is shown that the models a〉λ1,c〉λ1（-dθ2α/1＋mθ2α）md the coexistence solution is linear sta-bility if c〉λ1

关 键 词：捕食-食饵模型 稳定性 不动点指数 

分 类 号：O175.26[理学—数学]