GLOBAL STABILITY AND HOPF BIFURCATION ON A PREDATOR-PREY SYSTEM WITH DIFFUSION AND DELAYS

被引：2

作者：

Wang, Yuquan ^{[1
]}

机构：

[1] Nanjing Univ Finance & Econ, Dept Appl Math, Nanjing 210003, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2008年 / 38卷 / 05期

关键词：

Holling II functional response; delay; permanence; global stability; Hopf bifurcation;

D O I：

10.1216/RMJ-2008-38-5-1685

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper a predator-prey system with diffusion and two delays is considered, where the time delays are regarded as parameters. Its dynamics are studied in terms of permanence analysis and Hopf bifurcation analysis. By constructing a suitable Lyapunov function, sufficient conditions are obtained for both local and global stability of the positive equilibrium. An example is presented to show the main conclusion.

引用

页码：1685 / 1703

页数：19

共 12 条

[1]

CUI JA, 2004, ACTA MATH SINICA, V47, P512

[2]

[崔景安 Cui Jingan], 2005, [数学学报, Acta Mathematica Sinica], V48, P479

[3]

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

[4]

[桂占吉 Gui Zhanji], 2005, [系统科学与数学, Journal of Systems Science and Mathematical Sciences], V25, P50

[5] PREDATOR-PREY DYNAMICS IN MODELS OF PREY DISPERSAL IN 2-PATCH ENVIRONMENTS [J].

KUANG, Y ;

TAKEUCHI, Y .

MATHEMATICAL BIOSCIENCES, 1994, 120 (01) :77-98

[6]

LUO M, 1997, J BIOMATH, V12, P52

[7]

SONG X, 1988, COMPUT MATH APPL, V35, P33

[8]

[宋永利 Song Yongli], 2004, [数学年刊. A辑, Chinese Annals of Mathematics, Ser. A], V25, P783

[9] GLOBAL STABILITY IN GENERALIZED LOTKA-VOLTERRA DIFFUSION-SYSTEMS [J].

TAKEUCHI, Y .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1986, 116 (01) :209-221

[10]

[王育全 Wang Yuquan], 2006, [数学物理学报. A辑, Acta Mathematica Scientia], V26, P410

← 1 2 →