Persistence and stability in general nonautonomous single-species Kolmogorov systems with delays

被引：15

作者：

Teng, Zhidong ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2007年 / 8卷 / 01期

基金：

中国国家自然科学基金;

关键词：

single species; nonautonomous system; Kolmogorov system; delay; persistence; global asymptotic stability; positive periodic solution;

D O I：

10.1016/j.nonrwa.2005.08.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the general nonautonomous single-species Kolmogorov systems with delays. The sufficient conditions on the persistence and permanence of species, global asymptotic stability and the existence of positive periodic solutions are established. As applications of these results, the permanence, global asymptotic stability and the existence of positive periodic solutions for a series of special single-species growth systems with delays are discussed. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：230 / 248

页数：19

共 25 条

[1] ULTIMATE BOUNDS AND GLOBAL ASYMPTOTIC STABILITY FOR DIFFERENTIAL-DELAY EQUATIONS [J].

CAO, YL ;

GARD, TC .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1995, 25 (01) :119-131

[2] Periodic solutions of a delayed periodic logistic equation [J].

Chen, YM .

APPLIED MATHEMATICS LETTERS, 2003, 16 (07) :1047-1051

[3] Global attractivity in scalar delayed differential equations with applications to population models [J].

Faria, T .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 289 (01) :35-54

[4] PERIODIC-SOLUTIONS OF SINGLE-SPECIES MODELS WITH PERIODIC DELAY [J].

FREEDMAN, HI ;

WU, JH .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (03) :689-701

[5] ENVIRONMENTAL PERIODICITY AND TIME DELAYS IN A FOOD-LIMITED POPULATION-MODEL [J].

GOPALSAMY, K ;

KULENOVIC, MRS ;

LADAS, G .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1990, 147 (02) :545-555

[6]

Gopalsamy K., 2013, Stability and Oscillations in Delay Differential Equations of Population Dynamics, V74

[7]

Gopalsamy K., 1995, METHODS APPL ANAL, V2, P38

[8] NECESSARY AND SUFFICIENT CONDITIONS FOR THE OSCILLATIONS OF A MULTIPLICATIVE DELAY LOGISTIC EQUATION [J].

GRACE, SR ;

GYORI, I ;

LALLI, BS .

QUARTERLY OF APPLIED MATHEMATICS, 1995, 53 (01) :69-79

[9]

Grove E. A., 1993, DYNAM SYSTEMS APPL, V2, P243

[10] A new approach to the global asymptotic stability problem in a delay Lotka-Volterra differential equation [J].

Gyori, I .

MATHEMATICAL AND COMPUTER MODELLING, 2000, 31 (6-7) :9-28

← 1 2 3 →