Global stability and Hopf bifurcation of a plankton model with time delay

被引：8

作者：

Li, Lin ^{[1
]}

Liu, Zhicheng ^{[1
]}

机构：

[1] Capital Med Univ, Sch Biomed Engn, Beijing 100069, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 3-4期

关键词：

Plankton models; Differential delay equations; Global stability; SYSTEMS; FRONTS;

D O I：

10.1016/j.na.2009.09.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A differential delay equation model with a discrete time delay and a distributed time delay is introduced to simulate zooplankton-nutrient interaction. The differential inequalities' methods and standard Hopf bifurcation analysis are applied. Some sufficient conditions are obtained for persistence and for the global stability of the unique positive steady state, respectively. It was shown that there is a Hopf bifurcation in the model by using the discrete time delay as a bifurcation parameter. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1737 / 1745

页数：9

共 17 条

[1]

ARINO O, 2000, NONLINEAR ANAL-REAL, V1, P68

[2]

BERETTA E, 1991, J MATH BIOL, V85, P99

[3] UNIFORMLY PERSISTENT SYSTEMS [J].

BUTLER, G ;

FREEDMAN, HI ;

WALTMAN, P .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 96 (03) :425-430

[4] TIME-LAG AND CO-OPERATIVITY IN THE TRANSIENT GROWTH DYNAMICS OF MICROALGAE [J].

CUNNINGHAM, A ;

NISBET, RM .

JOURNAL OF THEORETICAL BIOLOGY, 1980, 84 (02) :189-203

[5]

Cushing J. M., 2013, Integrodifferential Equations and Delay Models in Population Dynamics, DOI DOI 10.1007/978-3-642-93073-7

[6] Plankton production in tidal fronts: A model of Georges Bank in summer [J].

Franks, PJS ;

Chen, CS .

JOURNAL OF MARINE RESEARCH, 1996, 54 (04) :631-651

[7] Phytoplankton patches at fronts: A model of formation and response to wind events [J].

Franks, PJS ;

Walstad, LJ .

JOURNAL OF MARINE RESEARCH, 1997, 55 (01) :1-29

[8]

GOPALSAMY K, 1983, B MATH BIOL, V45, P295, DOI 10.1016/S0092-8240(83)80058-5

[9] Spatio-temporal delays in a nutrient-plankton model on a finite domain: linear stability and bifurcations [J].

Gourley, SA ;

Ruan, S .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 145 (2-3) :391-412

[10]

Hale J.K., 1977, THEORY FUNCTIONAL DI

← 1 2 →