Persistence and global stability in a predator-prey system with delay

被引：4

作者：

Gamez, Manuel

Martinez, Clotilde ^{[1
]}

机构：

[1] Univ Granada, Fac Econ & Business Sci, Dept Appl Math, E-18071 Granada, Spain

[2] Univ Almeria, Dept Stat & Appl Math, Almeria 04120, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2006年 / 16卷 / 10期

关键词：

delayed Lotka-Volterra systems; global asymptotic stability; bifurcation; persistence; extinction;

D O I：

10.1142/S0218127406016549

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, several sufficient conditions are established for the persistence and extinction in a Lotka-Volterra system with time delay. Based on the use of Lyapunov functionals techniques, necessary and sufficient conditions are also given for global asymptotic stability of the positive equilibrium for autonomous systems.

引用

页码：2915 / 2922

页数：8

共 50 条

[1] Persistence and global stability for delay nonautonomous predator-prey system
Zhou, Sheng-Hua
Liu, Shu-Yun
Beijing Gongye Daxue Xuebao / Journal of Beijing University of Technology, 2007, 33 (08): : 874 - 877
[2] Persistence and global stability for nonautonomous predator-prey system with diffusion and time delay
Song, XY
Chen, LS
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 35 (06) : 33 - 40
[3] GLOBAL STABILITY OF A PREDATOR-PREY SYSTEM
LIOU, LP
CHENG, KS
JOURNAL OF MATHEMATICAL BIOLOGY, 1988, 26 (01) : 65 - 71
[4] GLOBAL STABILITY OF A PREDATOR-PREY SYSTEM
HSU, SB
MATHEMATICAL BIOSCIENCES, 1978, 39 (1-2) : 1 - 10
[5] PERSISTENCE AND GLOBAL STABILITY FOR TWO-SPECIES NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY
陈凤德
史金麟
陈晓星
Annals of Differential Equations, 2004, (02) : 111 - 117
[6] Persistence and stability of a two-species predator-prey system with time delay
Liu, QM
Xu, R
Feng, HY
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2005, 12 (06): : 783 - 793
[7] Persistence and stability in a ratio-dependent predator-prey system with delay and harvesting
Maiti, Alakes
Patra, Bibek
Samanta, G. P.
NATURAL RESOURCE MODELING, 2007, 20 (04) : 575 - 600
[8] Stability with Impulsive Delay Predator-Prey System
Han, Jinghua
Liu, Gang
FUZZY INFORMATION AND ENGINEERING 2010, VOL 1, 2010, 78 : 777 - 782
[9] Persistence and Global Stability for Two-Species Predator-Prey System With Diffusion
LIU He\|long
Journal of Systems Science and Systems Engineering, 1999, (04) : 3 - 5
[10] Global stability of a generalized predator-prey system
Gao, Hailong
Li, Yanqiu
ICIC Express Letters, 2015, 9 (08): : 2291 - 2297

← 1 2 3 4 5 →