# [1]张艳芳,陈文彦.一类捕食模型正解的唯一性和稳定性[J].东南大学学报(自然科学版),2010,40(4):882-884.[doi:10.3969/j.issn.1001-0505.2010.04.041] 　Zhang Yanfang,Chen Wenyan.Uniqueness and stability of positive solutions to a predator-prey model[J].Journal of Southeast University (Natural Science Edition),2010,40(4):882-884.[doi:10.3969/j.issn.1001-0505.2010.04.041] 点击复制 一类捕食模型正解的唯一性和稳定性() 分享到： var jiathis_config = { data_track_clickback: true };

40

2010年第4期

882-884

2010-07-20

## 文章信息/Info

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

Author(s):
Department of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

O175.25
DOI:
10.3969/j.issn.1001-0505.2010.04.041

Abstract:
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.

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