Global convergence of a reaction-diffusion predator-prey model with stage structure and nonlocal delays

被引：9
作者：
Xu, Rui [1 ]
Chaplain, M. A. J.
Davidson, F. A.
机构：
[1] Shijiazhuang Mech Engn Coll, Inst Appl Math, Shijiazhuang 050003, Peoples R China
[2] Yuncheng Univ, Dept Appl Math, Yuncheng 044000, Shanxi, Peoples R China
[3] Univ Dundee, Dept Math, Dundee DD1 4HN, Scotland
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2007年 / 53卷 / 05期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
stage structure; reaction-diffusion; nonlocal delay; steady-state solution; global convergence;
D O I：
10.1016/j.camwa.2007.02.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a Lotka-Volterra type reaction-diffusion predator-prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results. (c) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：770 / 788
页数：19
相关论文
共 28 条
[1]  
Adams R., 1975, Sobolev Spaces
[2]   SPACE-LIMITED RECRUITMENT IN OPEN SYSTEMS - THE IMPORTANCE OF TIME DELAYS [J].
BENCE, JR ;
NISBET, RM .
ECOLOGY, 1989, 70 (05) :1434-1441
[3]   Instability in diffusive ecological models with nonlocal delay effects [J].
Boushaba, K ;
Ruan, S .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 258 (01) :269-286
[4]   SPATIAL STRUCTURES AND PERIODIC TRAVELING WAVES IN AN INTEGRODIFFERENTIAL REACTION-DIFFUSION POPULATION-MODEL [J].
BRITTON, NF .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1990, 50 (06) :1663-1688
[5]  
CHEN L, 1988, MODELLING METHODS MA
[6]  
Cui JA, 2004, DISCRETE CONT DYN-B, V4, P547
[7]   The effect of dispersal on population growth with stage-structure [J].
Cui, JA ;
Chen, LS ;
Wang, WD .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 39 (1-2) :91-102
[8]   Effects of diffusion on a stage-structured population in a polluted environment [J].
Duan, LX ;
Lu, QS ;
Yang, ZZ ;
Chen, LS .
APPLIED MATHEMATICS AND COMPUTATION, 2004, 154 (02) :347-359
[9]   Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model [J].
Gourley, SA ;
Ruan, SG .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 35 (03) :806-822
[10]   Spatio-temporal delays in a nutrient-plankton model on a finite domain: linear stability and bifurcations [J].
Gourley, SA ;
Ruan, S .
APPLIED MATHEMATICS AND COMPUTATION, 2003, 145 (2-3) :391-412
123