A predator-prey model with generic birth and death rates for the predator and Beddington-DeAngelis functional response

被引：9

作者：

Ivanov, Tihomir ^{[1
,2
]}

Dimitrova, Neli ^{[1
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bonchev Str Bl 8, BU-1113 Sofia, Bulgaria

[2] Univ Sofia, Fac Math & Informat, 5 James Bourchier Blvd, Sofia 1164, Bulgaria

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2017年 / 133卷

关键词：

Predator-prey model; Beddington-DeAngelis response; Generic birth and death rates for the predator; Stability analysis; Numerical simulation; SYSTEM; INTERFERENCE; STABILITY; DYNAMICS;

D O I：

10.1016/j.matcom.2015.08.003

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We study a predator-prey model with a Beddington-DeAngelis response function and generic birth and death rates for the predator. The mathematical analysis of the model includes existence and uniqueness of positive solutions, their uniform boundedness, existence and global stability of equilibrium points. Numerical simulation confirms the theoretical results. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：111 / 123

页数：13

共 26 条

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

ARDITI, R ;

GINZBURG, LR .

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

[2]

Arditi R., 2012, How Species Interact: Altering the Standard View on Trophic Ecology, DOI [10.1093/acprof:osobl/9780199913831.001.0001, DOI 10.1093/ACPROF:OSOBL/9780199913831.001.0001]

[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] THE ORIGINS AND EVOLUTION OF PREDATOR PREY THEORY [J].

BERRYMAN, AA .

ECOLOGY, 1992, 73 (05) :1530-1535

[5]

Brauer F., 2012, Texts in Applied Mathematics, V40

[6] MODEL FOR TROPHIC INTERACTION [J].

DEANGELIS, DL ;

GOLDSTEIN, RA ;

ONEILL, RV .

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

[7] PERSISTENCE IN MODELS OF 3 INTERACTING PREDATOR-PREY POPULATIONS [J].

FREEDMAN, HI ;

WALTMAN, P .

MATHEMATICAL BIOSCIENCES, 1984, 68 (02) :213-231

[8] A detailed study of the Beddington-DeAngelis predator-prey model [J].

Haque, Mainul .

MATHEMATICAL BIOSCIENCES, 2011, 234 (01) :1-16

[9] Ratio-Dependent Predator-Prey Models of Interacting Populations [J].

Haque, Mainul .

BULLETIN OF MATHEMATICAL BIOLOGY, 2009, 71 (02) :430-452

[10] ON THE DYNAMICS OF TWO-CONSUMERS-ONE-RESOURCE COMPETING SYSTEMS WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE [J].

Hsu, Sze-Bi ;

Ruan, Shigui ;

Yang, Ting-Hui .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (09) :2331-2353

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