中文摘要：

讨论了一类具有饱和与竞争项的捕食模型,其中边界条件为齐次Dirichlet边界条件.主要分析了当竞争系数充分大时正解的性质.首先,利用标准的正则性理论和嵌入定理,得到了正解的渐近性.其次,利用隐函数定理推导出正解的唯一性.最后,结合线性化稳定性理论得到正解的稳定性.结果表明,猎物之间的强竞争限制了种群的多样性,并导致2种群的捕食系统更加稳定.

英文摘要：

A predator-prey model with predator saturation and competition under homogeneous Dirichlet boundary condition is discussed.The property of positive solutions is mainly concerned when the competitive parameter is large enough.Firstly,using the standard regularity theory and embedding theorem,the asymptotic behavior of positive solutions is given.Secondly,by virtue of the implicit function theorem the uniqueness is investigated.Moreover,the stability is obtained using the linear stability theory.It turns out that the species diversity is limited and the predatory system is more stable when the interference between the predator species is strong.