Effect of prey-taxis and diffusion on positive steady states for a predator-prey system

被引：7

作者：

Gao, Jianping ^{[1
]}

Guo, Shangjiang ^{[1
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 10期

关键词：

fixed-point index theory; positive steady state; predator-prey system; prey-taxis; PATTERN-FORMATION; GLOBAL BIFURCATION; MODEL; COMPETITION; CHEMOTAXIS; EXISTENCE; ADVECTION; EQUATIONS; VOLTERRA;

D O I：

10.1002/mma.4847

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a generalized predator-prey system with prey-taxis under the Neumann boundary condition. We investigate the local and global asymptotical stability of constant steady states (including trivial, semitrivial, and interior constant steady states). On the basis of a priori estimate and the fixed-point index theory, several sufficient conditions for the nonexistence/existence of nonconstant positive solutions are given.

引用

页码：3570 / 3587

页数：18

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