Persistence and global stability of a ratio-dependent predator-prey model with stage structure

Rui Xu; M. A. J. Chaplain; F. A. Davidson

doi:10.1016/j.amc.2003.10.012

Persistence and global stability of a ratio-dependent predator-prey model with stage structure

Rui Xu, M. A. J. Chaplain, F. A. Davidson

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

54 Citations (Scopus)

Abstract

A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.

Original language	English
Pages (from-to)	729-744
Number of pages	16
Journal	Applied Mathematics and Computation
Volume	158
Issue number	3
DOIs	https://doi.org/10.1016/j.amc.2003.10.012
Publication status	Published - Nov 2004

Keywords

Ratio-dependence
Predator-prey model
Stage structure
Uniform persistence
Global stability

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10.1016/j.amc.2003.10.012

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title = "Persistence and global stability of a ratio-dependent predator-prey model with stage structure",

abstract = "A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.",

keywords = "Ratio-dependence, Predator-prey model, Stage structure, Uniform persistence, Global stability",

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

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AU - Chaplain, M. A. J.

AU - Davidson, F. A.

N1 - dc.publisher: Elsevier

PY - 2004/11

Y1 - 2004/11

N2 - A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.

AB - A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.

KW - Ratio-dependence

KW - Predator-prey model

KW - Stage structure

KW - Uniform persistence

KW - Global stability

U2 - 10.1016/j.amc.2003.10.012

DO - 10.1016/j.amc.2003.10.012

M3 - Article

SN - 0096-3003

VL - 158

SP - 729

EP - 744

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 3

ER -

Persistence and global stability of a ratio-dependent predator-prey model with stage structure

Abstract

Keywords

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