Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes

被引：539

作者：

Aziz-Alaoui, MA ^{[1
]}

Okiye, MD ^{[1
]}

机构：

[1] Univ Le Havre, Lab Math Appl, F-76058 Le Havre, France

来源：

APPLIED MATHEMATICS LETTERS | 2003年 / 16卷 / 07期

关键词：

differential equations; Leslie-Gower; Holling-type-II; boundedness; Lyapunov function; stability;

D O I：

10.1016/S0893-9659(03)90096-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a two-dimensional continuous time dynamical system modeling a predator-prey food chain, and based on a modified version of the Leslie-Gower scheme and on the Holling-type II scheme. The main result is given in terms of boundedness of solutions, existence of an attracting set and global stability of the coexisting interior equilibrium. (C) 2003 Elsevier Ltd. All rights reserved.

引用

页码：1069 / 1075

页数：7

共 9 条

[1] Study of a Leslie-Gower-type tritrophic population model [J].

Aziz-Alaoui, MA .

CHAOS SOLITONS & FRACTALS, 2002, 14 (08) :1275-1293

[2] SPECIALIST PREDATORS, GENERALIST PREDATORS, AND THE MICROTINE RODENT CYCLE [J].

HANSKI, I ;

HANSSON, L ;

HENTTONEN, H .

JOURNAL OF ANIMAL ECOLOGY, 1991, 60 (01) :353-367

[3] A Lyapunov function for Leslie-Gower predator-prey models [J].

Korobeinikov, A .

APPLIED MATHEMATICS LETTERS, 2001, 14 (06) :697-699

[4] SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS [J].

LESLIE, PH .

BIOMETRIKA, 1948, 35 (3-4) :213-245

[5] THE PROPERTIES OF A STOCHASTIC MODEL FOR THE PREDATOR-PREY TYPE OF INTERACTION BETWEEN 2 SPECIES [J].

LESLIE, PH ;

GOWER, JC .

BIOMETRIKA, 1960, 47 (3-4) :219-234

[6] Should all the species of a food chain be counted to investigate the global dynamics? [J].

Letellier, C ;

Aguirre, LA ;

Maquet, J ;

Aziz-Alaoui, MA .

CHAOS SOLITONS & FRACTALS, 2002, 13 (05) :1099-1113

[7] Analysis of the dynamics of a realistic ecological model [J].

Letellier, C ;

Aziz-Alaoui, MA .

CHAOS SOLITONS & FRACTALS, 2002, 13 (01) :95-107

[8]

PIELOU E C, 1969, P286

[9] Why chaos is rarely observed in natural populations [J].

Upadhyay, RK ;

Rai, VK .

CHAOS SOLITONS & FRACTALS, 1997, 8 (12) :1933-1939

← 1 →