Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure

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

doi:10.1016/j.jmaa.2004.08.062

Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure

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

Applied Mathematics

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

Abstract

A periodic ratio-dependent predator?prey model with time delays and stage structure for both prey and predator is investigated. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age, and that immature predators do not have the ability to attack prey. Sufficient conditions are derived for the permanence and existence of positive periodic solutions of the model. Numerical simulations are presented to illustrate the feasibility of our main results

Original language	English
Pages (from-to)	602-621
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	303
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2004.08.062
Publication status	Published - 2005

Keywords

Stage structure
Ratio-dependence
Permanence
Periodic solution
Time delay

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10.1016/j.jmaa.2004.08.062

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title = "Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure",

abstract = "A periodic ratio-dependent predator?prey model with time delays and stage structure for both prey and predator is investigated. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age, and that immature predators do not have the ability to attack prey. Sufficient conditions are derived for the permanence and existence of positive periodic solutions of the model. Numerical simulations are presented to illustrate the feasibility of our main results",

keywords = "Stage structure, Ratio-dependence, Permanence, Periodic solution, Time delay",

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

year = "2005",

doi = "10.1016/j.jmaa.2004.08.062",

language = "English",

volume = "303",

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journal = "Journal of Mathematical Analysis and Applications",

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T1 - Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure

AU - Xu, Rui

AU - Chaplain, M. A. J.

AU - Davidson, F. A.

PY - 2005

Y1 - 2005

N2 - A periodic ratio-dependent predator?prey model with time delays and stage structure for both prey and predator is investigated. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age, and that immature predators do not have the ability to attack prey. Sufficient conditions are derived for the permanence and existence of positive periodic solutions of the model. Numerical simulations are presented to illustrate the feasibility of our main results

AB - A periodic ratio-dependent predator?prey model with time delays and stage structure for both prey and predator is investigated. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age, and that immature predators do not have the ability to attack prey. Sufficient conditions are derived for the permanence and existence of positive periodic solutions of the model. Numerical simulations are presented to illustrate the feasibility of our main results

KW - Stage structure

KW - Ratio-dependence

KW - Permanence

KW - Periodic solution

KW - Time delay

U2 - 10.1016/j.jmaa.2004.08.062

DO - 10.1016/j.jmaa.2004.08.062

M3 - Article

SN - 0022-247X

VL - 303

SP - 602

EP - 621

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure

Abstract

Keywords

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