Qualitative analysis for a diffusive predator-prey model

被引：17

作者：

Chen, Bin ^{[1
,2
]}

Wang, Mingxin ^{[2
]}

机构：

[1] Yancheng Teachers Coll, Dept Math, Yancheng 224001, Peoples R China

[2] Southeast Univ, Dept Math, Nanjing 210018, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2008年 / 55卷 / 03期

基金：

中国国家自然科学基金;

关键词：

predator-prey model; iteration technique; stability; stationary patterns;

D O I：

10.1016/j.camwa.2007.03.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the qualitative properties of a diffusive predator-prey model subject to the homogeneous Neumann boundary condition. By a comparison argument and iteration technique, under some hypotheses we prove that the positive constant steady state is globally asymptotically stable. We also establish the existence and non-existence of non-constant positive steady states (stationary patterns) by use of the degree theory and the a priori estimates. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：339 / 355

页数：17

共 25 条

[1] Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes [J].

Aziz-Alaoui, MA ;

Okiye, MD .

APPLIED MATHEMATICS LETTERS, 2003, 16 (07) :1069-1075

[2] DECAY TO UNIFORM STATES IN ECOLOGICAL INTERACTIONS [J].

BROWN, PN .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1980, 38 (01) :22-37

[3] Practical persistence in ecological models via comparison methods [J].

Cantrell, RS ;

Cosner, C .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1996, 126 :247-272

[4] Stationary patterns created by cross-diffusion for the competitor-competitor-mutualist model [J].

Chen, WY ;

Peng, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 291 (02) :550-564

[5] ON POSITIVE SOLUTIONS OF SOME PAIRS OF DIFFERENTIAL-EQUATIONS [J].

DANCER, EN .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 284 (02) :729-743

[6] CONVERGENCE TO HOMOGENEOUS EQUILIBRIUM STATE FOR GENERALIZED VOLTERRA-LOTKA SYSTEMS WITH DIFFUSION [J].

DEMOTTONI, P ;

ROTHE, F .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1979, 37 (03) :648-663

[7] A diffusive predator-prey model in heterogeneous environment [J].

Du, YH ;

Hsu, SB .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 203 (02) :331-364

[8] Qualitative behaviour of positive solutions of a predator-prey model: effects of saturation [J].

Du, YH ;

Lou, Y .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2001, 131 :321-349

[9] Some uniqueness and exact multiplicity results for a predator-prey model [J].

Du, YH ;

Lou, Y .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (06) :2443-2475

[10] Asymptotic behaviour of positive steady states to a predator-prey model [J].

Du, Yihong ;

Wang, Mingxin .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2006, 136 :759-778

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