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

Rui Xu; M. A. J. Chaplain

doi:10.1016/S0096-3003(01)00111-4

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

Rui Xu, M. A. J. Chaplain

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

25 Citations (Scopus)

Abstract

A delayed three-species predator–prey food-chain model with Michaelis–Menten type functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive equilibrium of the system.

Original language	English
Pages (from-to)	441-455
Number of pages	15
Journal	Applied Mathematics and Computation
Volume	130
Issue number	2-3
DOIs	https://doi.org/10.1016/S0096-3003(01)00111-4
Publication status	Published - Aug 2002

Keywords

Delay
Uniform persistence
Stability
Lyapunov functional

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10.1016/S0096-3003(01)00111-4

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

abstract = "A delayed three-species predator–prey food-chain model with Michaelis–Menten type functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive equilibrium of the system.",

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

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

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year = "2002",

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

AU - Xu, Rui

AU - Chaplain, M. A. J.

N1 - dc.publisher: Elsevier Science

PY - 2002/8

Y1 - 2002/8

N2 - A delayed three-species predator–prey food-chain model with Michaelis–Menten type functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive equilibrium of the system.

AB - A delayed three-species predator–prey food-chain model with Michaelis–Menten type functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive equilibrium of the system.

KW - Delay

KW - Uniform persistence

KW - Stability

KW - Lyapunov functional

U2 - 10.1016/S0096-3003(01)00111-4

DO - 10.1016/S0096-3003(01)00111-4

M3 - Article

SN - 0096-3003

VL - 130

SP - 441

EP - 455

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2-3

ER -

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

Abstract

Keywords

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