Uniqueness and stability of a predator-prey model with C-M functional response

被引：20

作者：

Li, Shanbing ^{[1
]}

Wu, Jianhua ^{[1
]}

Dong, Yaying ^{[2
]}

机构：

[1] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Peoples R China

[2] NW Univ Xian, Sch Math, Xian 710069, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2015年 / 69卷 / 10期

关键词：

Crowley-Martin functional response; Lyapunov-Schmidt procedure; Perturbation technique; Uniqueness; Stability; POSITIVE STEADY-STATES; ASYMPTOTIC-BEHAVIOR; GLOBAL STABILITY; MULTIPLICITY; INTERFERENCE; SYSTEM; BIFURCATION; DIFFUSION;

D O I：

10.1016/j.camwa.2015.03.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with positive solutions of a predator-prey model with Crowley-Martin functional response under Dirichlet boundary conditions. First, we establish the existence of positive solutions when (a, c) is close to (lambda(1), lambda(1)). Next, the stability properties of nonnegative solutions are discussed by spectral analysis. In addition, we obtain a complete understanding of the uniqueness and non-uniqueness of positive solutions by the Lyapunov-Schmidt procedure and the perturbation technique. At last, some numerical simulations are presented to supplement the analytic results in one dimension. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：1080 / 1095

页数：16

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