Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response

被引：115

作者：

Hwang, TW ^{[1
]}

机构：

[1] Kaohsiung Normal Univ, Dept Math, Kaohsiung 802, Taiwan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2004年 / 290卷 / 01期

关键词：

Beddington-DeAngelis predator-prey model; functional response; global stability; limit cycles;

D O I：

10.1016/j.jmaa.2003.09.073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The goal of this paper is to establish the uniqueness of limit cycles of the predator-prey systems with Beddington-DeAngelis functional response. Through a change of variables, the predator-prey system can be transformed into a better studied Gause-type predator-prey system. As a result, the uniqueness of limit cycles can be solved. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：113 / 122

页数：10

共 9 条

[1] The nature of predation: prey dependent, ratio dependent or neither? [J].

Abrams, PA ;

Ginzburg, LR .

TRENDS IN ECOLOGY & EVOLUTION, 2000, 15 (08) :337-341

[2] COUPLING IN PREDATOR PREY DYNAMICS - RATIO-DEPENDENCE [J].

ARDITI, R ;

GINZBURG, LR .

JOURNAL OF THEORETICAL BIOLOGY, 1989, 139 (03) :311-326

[3] MUTUAL INTERFERENCE BETWEEN PARASITES OR PREDATORS AND ITS EFFECT ON SEARCHING EFFICIENCY [J].

BEDDINGTON, JR .

JOURNAL OF ANIMAL ECOLOGY, 1975, 44 (01) :331-340

[4] On the dynamics of predator-prey models with the Beddington-DeAngelis functional response [J].

Cantrell, RS ;

Cosner, C .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 257 (01) :206-222

[5] Effects of spatial grouping on the functional response of predators [J].

Cosner, C ;

DeAngelis, DL ;

Ault, JS ;

Olson, DB .

THEORETICAL POPULATION BIOLOGY, 1999, 56 (01) :65-75

[6] MODEL FOR TROPHIC INTERACTION [J].

DEANGELIS, DL ;

GOLDSTEIN, RA ;

ONEILL, RV .

ECOLOGY, 1975, 56 (04) :881-892

[7] Global analysis of the predator-prey system with Beddington-DeAngelis functional response [J].

Hwang, TW .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 281 (01) :395-401

[8] Uniqueness of the limit cycle for cause-type predator-prey systems [J].

Hwang, TW .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 238 (01) :179-195

[9]

KUANG Y, 1988, Mathematical Biosciences, V88, P67, DOI 10.1016/0025-5564(88)90049-1

← 1 →