Uniqueness and stability of positive steady state solutions for a ratio-dependent predator-prey system with a crowding term in the prey equation

被引：14
|
作者：
Zeng, Xianzhong [1 ]
Zhang, Jianchen [1 ]
Gu, Yonggeng [2 ]
机构：
[1] Hunan Univ Sci & Technol, Sch Math & Comp Sci, Xiangtan 411201, Peoples R China
[2] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2015年 / 24卷
基金：
湖南省自然科学基金; 中国国家自然科学基金;
关键词：
Ratio-dependent predator-prey system; Crowding effect; Existence; Uniqueness; Stability; UP BOUNDARY SOLUTION; CROSS-DIFFUSION; PRINCIPAL EIGENVALUES; QUALITATIVE-ANALYSIS; ASYMPTOTIC-BEHAVIOR; LOGISTIC EQUATIONS; STATIONARY PROBLEM; COMPETITION MODEL; MAXIMUM PRINCIPLE; POPULATION-MODELS;
D O I：
10.1016/j.nonrwa.2015.02.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with a ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrate some special behaviors of solutions to the system which the coexistence states of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we demonstrate that under some conditions, the positive steady state solution of the predator-prey system with a crowding term in the prey equation is unique and stable. Our result is different from those ones of the predator-prey systems without the crowding terms. (C) 2015 Elsevier Ltd. All rights reserved.
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页码：163 / 174
页数：12
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