Steady states of a predator-prey model with prey-taxis

被引：47
作者：
Li, Chenglin [1 ,2 ]
Wang, Xuhuang [2 ]
Shao, Yuanfu [3 ]
机构：
[1] Honghe Univ, Dept Math, Mengzi 661100, Yunnan, Peoples R China
[2] Baoshan Univ, Sch Math, Baoshan 678000, Peoples R China
[3] Guilin Univ Technol, Guangxi 541000, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 97卷
关键词：
Prey-taxis; Steady states; NONMONOTONIC FUNCTIONAL-RESPONSE; COEXISTENCE STATES; SYSTEM; BIFURCATION; DIFFUSION; PATTERNS;
D O I：
10.1016/j.na.2013.11.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the steady states of a predator-prey model with prey-taxis incorporating Holling type II functional response under the homogeneous Neumann boundary condition. The stability of equilibrium points and the existence of non-constant steady states are investigated. We obtain that the prey-tactic sensitivity coefficient delays the stability of the unique positive constant solution, but for other equilibrium points' stability, the prey-tactic sensitivity coefficient does not influence on it. Furthermore, we derive some sufficient conditions relative to the prey-tactic sensitivity coefficient which confines the existence of steady states and find that even if the interaction coefficient is sufficiently large, there also exist non-constant positive steady states under some conditions. (C) 2013 Elsevier Ltd. All rights reserved.
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页码：155 / 168
页数：14
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