Persistence and global stability in a delayed predator-prey system with Holling-type functional response

Rui Xu; Lansun Chen; M. A. J. Chaplain

doi:10.1017/S1446181100013729

Persistence and global stability in a delayed predator-prey system with Holling-type functional response

Rui Xu, Lansun Chen, M. A. J. Chaplain

Applied Mathematics

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

Abstract

A delayed predator-prey system with Holling type III functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of suitable Lyapunov functionals, sufficient conditions are derived for the local and global asymptotic stability of a positive equilibrium of the system. Numerical simulations are presented to illustrate the feasibility of our main results.

Original language	English
Pages (from-to)	121-141
Number of pages	21
Journal	ANZIAM Journal
Volume	46
Issue number	1
DOIs	https://doi.org/10.1017/S1446181100013729
Publication status	Published - 2004

Keywords

Global stability
Persistence
Predator-prey model

Access to Document

10.1017/S1446181100013729

Cite this

@article{2c38f2a979f848b29a9cf89a29a6cc4e,

title = "Persistence and global stability in a delayed predator-prey system with Holling-type functional response",

abstract = "A delayed predator-prey system with Holling type III functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of suitable Lyapunov functionals, sufficient conditions are derived for the local and global asymptotic stability of a positive equilibrium of the system. Numerical simulations are presented to illustrate the feasibility of our main results.",

keywords = "Global stability, Persistence, Predator-prey model",

author = "Rui Xu and Lansun Chen and Chaplain, {M. A. J.}",

year = "2004",

doi = "10.1017/S1446181100013729",

language = "English",

volume = "46",

pages = "121--141",

journal = "ANZIAM Journal",

issn = "1446-1811",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - Persistence and global stability in a delayed predator-prey system with Holling-type functional response

AU - Xu, Rui

AU - Chen, Lansun

AU - Chaplain, M. A. J.

PY - 2004

Y1 - 2004

N2 - A delayed predator-prey system with Holling type III functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of suitable Lyapunov functionals, sufficient conditions are derived for the local and global asymptotic stability of a positive equilibrium of the system. Numerical simulations are presented to illustrate the feasibility of our main results.

AB - A delayed predator-prey system with Holling type III functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of suitable Lyapunov functionals, sufficient conditions are derived for the local and global asymptotic stability of a positive equilibrium of the system. Numerical simulations are presented to illustrate the feasibility of our main results.

KW - Global stability

KW - Persistence

KW - Predator-prey model

U2 - 10.1017/S1446181100013729

DO - 10.1017/S1446181100013729

M3 - Article

SN - 1446-1811

VL - 46

SP - 121

EP - 141

JO - ANZIAM Journal

JF - ANZIAM Journal

IS - 1

ER -

Persistence and global stability in a delayed predator-prey system with Holling-type functional response

Abstract

Keywords

Access to Document

Fingerprint

Cite this