Coexistence states of a predator-prey model with cross-diffusion

被引：11
|
作者：
Yuan, Hailong [1 ]
Wu, Jianhua [1 ]
Jia, Yunfeng [1 ]
Nie, Hua [1 ]
机构：
[1] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710119, Shaanxi, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 41卷
关键词：
Predator-prey model; Cross-diffusion; Coexistence states; Multiplicity; Bifurcation; POSITIVE STEADY-STATES; GLOBAL BIFURCATION; PROTECTION ZONE; SYSTEM; EQUATIONS;
D O I：
10.1016/j.nonrwa.2017.10.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with positive solutions of a predator-prey model with cross diffusion. By virtue of the Leray-Schauder degree theory and the bifurcation theory, some sufficient conditions for the existence of positive solutions of the system are established. In particular, we derive the multiplicity results when some parameters are suitably large. Moreover, the existence and stability of nonconstant solutions are studied by the techniques of space decomposition and the implicit function theorem. Finally, the uniqueness of positive solution is studied when the spatial dimension is one. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：179 / 203
页数：25
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