A density-dependent predator-prey model of beddington-deangelis type

Haiyin Li; Zhikun She

A density-dependent predator-prey model of beddington-deangelis type

Haiyin Li^*
, Zhikun She

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this article, we study the dynamics of a density-dependent predator-prey system of Beddington-DeAngelis type. We obtain sufficient and necessary conditions for the existence of a unique positive equilibrium, the global attractiveness of the boundary equilibrium, and the permanence of the system, respectively. Moreover, we derive a sufficient condition for the lo- cally asymptotic stability of the positive equilibrium by the Lyapunov function theory and a sufficient condition for the global attractiveness of the positive equilibrium by the comparison theory.

Original language	English
Journal	Electronic Journal of Differential Equations
Volume	2014
State	Published - 16 Sep 2014

Keywords

Density dependence
Global attractiveness
Permanence
ω-limit set

Cite this

@article{4324ff52c862487ba6d8fb5e2335169e,

title = "A density-dependent predator-prey model of beddington-deangelis type",

abstract = "In this article, we study the dynamics of a density-dependent predator-prey system of Beddington-DeAngelis type. We obtain sufficient and necessary conditions for the existence of a unique positive equilibrium, the global attractiveness of the boundary equilibrium, and the permanence of the system, respectively. Moreover, we derive a sufficient condition for the lo- cally asymptotic stability of the positive equilibrium by the Lyapunov function theory and a sufficient condition for the global attractiveness of the positive equilibrium by the comparison theory.",

keywords = "Density dependence, Global attractiveness, Permanence, ω-limit set",

author = "Haiyin Li and Zhikun She",

note = "Publisher Copyright: {\textcopyright} 2014 Texas State University - San Marcos.",

year = "2014",

month = sep,

day = "16",

language = "英语",

volume = "2014",

journal = "Electronic Journal of Differential Equations",

issn = "1550-6150",

publisher = "Texas State University - San Marcos",

}

TY - JOUR

T1 - A density-dependent predator-prey model of beddington-deangelis type

AU - Li, Haiyin

AU - She, Zhikun

PY - 2014/9/16

Y1 - 2014/9/16

N2 - In this article, we study the dynamics of a density-dependent predator-prey system of Beddington-DeAngelis type. We obtain sufficient and necessary conditions for the existence of a unique positive equilibrium, the global attractiveness of the boundary equilibrium, and the permanence of the system, respectively. Moreover, we derive a sufficient condition for the lo- cally asymptotic stability of the positive equilibrium by the Lyapunov function theory and a sufficient condition for the global attractiveness of the positive equilibrium by the comparison theory.

AB - In this article, we study the dynamics of a density-dependent predator-prey system of Beddington-DeAngelis type. We obtain sufficient and necessary conditions for the existence of a unique positive equilibrium, the global attractiveness of the boundary equilibrium, and the permanence of the system, respectively. Moreover, we derive a sufficient condition for the lo- cally asymptotic stability of the positive equilibrium by the Lyapunov function theory and a sufficient condition for the global attractiveness of the positive equilibrium by the comparison theory.

KW - Density dependence

KW - Global attractiveness

KW - Permanence

KW - ω-limit set

UR - https://www.scopus.com/pages/publications/84907694739

M3 - 文章

AN - SCOPUS:84907694739

SN - 1550-6150

VL - 2014

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

A density-dependent predator-prey model of beddington-deangelis type

Abstract

Keywords

Other files and links

Fingerprint

Cite this