Predator-prey model of Beddington-DeAngelis type with maturation and gestation delays

被引：37

作者：

Liu, Shengqiang ^{[1
]}

Beretta, Edoardo ^{[2
]}

Breda, Dimitri ^{[3
]}

机构：

[1] Harbin Inst Technol, Nat Sci Res Ctr, Acad Fundamental & Interdisciplinary Sci, Harbin 150080, Peoples R China

[2] Univ Urbino, Ist Biomatemat, I-61029 Urbino, Italy

[3] Univ Udine, Dept Math & Comp Sci, I-33100 Udine, Italy

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 05期

关键词：

Predator-prey; Stage structure; Gestation delay; Beddington-DeAngelis; FUNCTIONAL-RESPONSE; SYSTEM; STABILITY; INTERFERENCE; PERSISTENCE; BIFURCATION; DYNAMICS;

D O I：

10.1016/j.nonrwa.2010.03.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A predator-prey model of Beddington-DeAngelis type with maturation and gestation delays is formulated and analyzed. This two-delay model is similar to the stage-structured model by Liu and Beretta [S. Liu, E. Beretta, Stage-structured predator-prey Model with the Beddington-DeAngelis functional response, SIAM J. Appl. Math. 66 (2006) 1101-1129] but contains an extra gestation delay term. Criteria for permanence and for predator extinction as well as the global attractiveness of the interior equilibrium are derived. The combined effects of the two delays and the degree of predator interference on the dynamical behaviors of the coexistence equilibrium are also studied both analytically and numerically. It is shown that complicated behaviors including chaotic and multi-periodic solutions may occur with the introduction of gestation delay, and that the predator interference can stabilize the system by simplifying the dynamical behaviors and enlarging the stability parameter fields. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：4072 / 4091

页数：20

共 23 条

[1] Invulnerable prey and the paradox of enrichment [J].

Abrams, PA ;

Walters, CJ .

ECOLOGY, 1996, 77 (04) :1125-1133

[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] Pseudospectral differencing methods for characteristic roots of delay differential equations [J].

Breda, D ;

Maset, S ;

Vermiglio, R .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2005, 27 (02) :482-495

[5]

Breda D, 2009, LECT NOTES CONTR INF, V388, P145, DOI 10.1007/978-3-642-02897-7_13

[6] An adaptive algorithm for efficient computation of level curves of surfaces [J].

Breda, Dimitri ;

Maset, Stefano ;

Vermiglio, Rossana .

NUMERICAL ALGORITHMS, 2009, 52 (04) :605-628

[7] 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

[8] TIME LAG IN POPULATION GROWTH RESPONSE OF ISOCHRYSIS GALBANA TO A VARIABLE NITRATE ENVIRONMENT [J].

CAPERON, J .

ECOLOGY, 1969, 50 (02) :188-&

[9] 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

[10] MODEL FOR TROPHIC INTERACTION [J].

DEANGELIS, DL ;

GOLDSTEIN, RA ;

ONEILL, RV .

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

← 1 2 3 →