On The Dynamics of a Predator-Prey Model with Delays and Diffusion

被引：0

作者：

Wang, Yuquan ^{[1
]}

Ma, Junying ^{[1
]}

机构：

[1] Nanjing Univ Finance & Econ, Dept Appl Math, Nanjing 210046, Peoples R China

来源：

PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II | 2010年

关键词：

Monod-Haldane functional response; time delay; diffusion; stability; Hopf bifurcation; GLOBAL STABILITY; SYSTEM; PERMANENCE; BIFURCATION; DISPERSAL;

D O I：

暂无

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, a delayed predator-prey system with Monod-Haldane functional response and diffusion is considered. The local stability and Hopf bifurcation problem are studied by the parameters analysis. Meanwhile, the sufficient conditions are obtained for global stability of a positive equilibrium by constructing a suitable Lyapunov function.

引用

页码：326 / 332

页数：7

共 16 条

[1] Bifurcations in a predator-prey model in patchy environment with diffusion [J].

Aly, S ;

Farkas, M .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2004, 5 (03) :519-526

[2] A MATHEMATICAL MODEL FOR CONTINUOUS CULTURE OF MICROORGANISMS UTILIZING INHIBITORY SUBSTRATES [J].

ANDREWS, JF .

BIOTECHNOLOGY AND BIOENGINEERING, 1968, 10 (06) :707-+

[3]

Barbalat I., 1959, Rev. Math. Pures Appl., V4, P267

[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] Analysis of a Monod-Haldene type food chain chemostat with periodically varying substrate [J].

Pang, Guoping ;

Wang, Fengyan ;

Chen, Lansun .

CHAOS SOLITONS & FRACTALS, 2008, 38 (03) :731-742

[7]

Ruan SG, 2000, SIAM J APPL MATH, V61, P1445

[8] Permanence and global attractivity of the food-chain system with Holling IV type functional response [J].

Shen, Chunxia .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 194 (01) :179-185

[9] KINETICS OF PHENOL OXIDATION BY WASHED CELLS [J].

SOKOL, W ;

HOWELL, JA .

BIOTECHNOLOGY AND BIOENGINEERING, 1981, 23 (09) :2039-2049

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

TAKEUCHI, Y .

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

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