Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks

Rui Xu; M. A. J. Chaplain

doi:10.1006/jmaa.2001.7701

Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks

Rui Xu, M. A. J. Chaplain

Applied Mathematics

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

Abstract

A delayed Gause-type predator?prey system without dominating instantaneous negative feedbacks is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing a suitable Lyapunov functional, sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system.

Original language	English
Pages (from-to)	148-162
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	265
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.2001.7701
Publication status	Published - 2002

Keywords

Uniform persistence
Stability
Delay
Lyapunov functional

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10.1006/jmaa.2001.7701

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title = "Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks",

abstract = "A delayed Gause-type predator?prey system without dominating instantaneous negative feedbacks is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing a suitable Lyapunov functional, sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system.",

keywords = "Uniform persistence, Stability, Delay, Lyapunov functional",

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

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AU - Xu, Rui

AU - Chaplain, M. A. J.

PY - 2002

Y1 - 2002

N2 - A delayed Gause-type predator?prey system without dominating instantaneous negative feedbacks is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing a suitable Lyapunov functional, sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system.

AB - A delayed Gause-type predator?prey system without dominating instantaneous negative feedbacks is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing a suitable Lyapunov functional, sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system.

KW - Uniform persistence

KW - Stability

KW - Delay

KW - Lyapunov functional

UR - https://www.scopus.com/pages/publications/0036153653

U2 - 10.1006/jmaa.2001.7701

DO - 10.1006/jmaa.2001.7701

M3 - Article

SN - 0022-247X

VL - 265

SP - 148

EP - 162

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks

Abstract

Keywords

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