On a Leslie-Gower predator-prey model incorporating a prey refuge

被引：147

作者：

Chen, Fengde ^{[1
]}

Chen, Liujuan ^{[2
]}

Xie, Xiangdong ^{[3
]}

机构：

[1] Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350002, Fujian, Peoples R China

[2] Fujian Educ Coll, Dept Math & Phys, Fuzhou 350002, Fujian, Peoples R China

[3] Ningde Teachers Coll, Dept Math, Ningde 352100, Fujian, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2009年 / 10卷 / 05期

关键词：

Leslis-Gower; Lyapunov function; Global stable; FUNCTIONAL-RESPONSE; II SCHEMES; STABILITY; SYSTEM;

D O I：

10.1016/j.nonrwa.2008.09.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a Leslie-Gower predator-prey model incorporating a prey refuge. By constructing a suitable Lyapunov function, we show that the unique positive equilibrium of the system is globally stable, which means that for this ecosystem, prey refuge has no influence on the persistent property of the system. Mathematic analysis shows that increasing the amount of refuge can increase prey densities. As far as the predator species is concerned, when the assumption a(1)r(2) <= a(2)b(1), holds, increasing the amount of prey refuge can decrease the predator densities; when the assumption a(1)r(2) > a(2)b(1) holds, there exists a threshold m*, such that for the prey refuge smaller than this threshold, increasing the amount of prey refuge can increase the predator densities and if the prey refuge is larger than the threshold, increasing the amount of prey refuge can decrease the predator densities. (C) 2009 Published by Elsevier Ltd

引用

页码：2905 / 2908

页数：4

共 16 条

[1] AGUIRRE P, NONLINEAR A IN PRESS
[2] Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes
Aziz-Alaoui, MA
Okiye, MD
[J]. APPLIED MATHEMATICS LETTERS, 2003, 16 (07) : 1069 - 1075
[3] Permanence, extinction and periodic solution of the predator-prey system with Beddington-DeAngelis functional response and stage structure for prey
Chen, Fengde
You, Minsheng
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (02) : 207 - 221
[4] On a delayed nonautonomous ratio-dependent predator-prey model with Holling type functional response and diffusion
Chen, Fengde
Shi, Jinlin
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 192 (02) : 358 - 369
[5] Dynamic consequences of prey refuges in a simple model system:: more prey, fewer predators and enhanced stability
González-Olivares, E
Ramos-Jiliberto, R
[J]. ECOLOGICAL MODELLING, 2003, 166 (1-2) : 135 - 146
[6] Hoy M.A., 1985, World Crop Pests, V1B, P229
[7] Stability analysis of a prey-predator model with holling type III response function incorporating a prey refuge
Huang, Yunjin
Chen, Fengde
Zhong, Li
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 182 (01) : 672 - 683
[8] Kar T. K., 2005, Communications in Nonlinear Science and Numerical Simulation, V10, P681, DOI 10.1016/j.cnsns.2003.08.006
[9] Kar TK, 2006, J COMPUT APPL MATH, V185, P19, DOI [10.1016/j.cam.2005.01.035, 10.1016/j.cam.20050.01.035]
[10] Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge
Ko, Wonlyul
Ryu, Kimun
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 231 (02) : 534 - 550

← 1 2 →