Periodic solution for a three-species Lotka-Volterra food-chain model with time delays

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

doi:10.1016/j.mcm.2004.10.011

Periodic solution for a three-species Lotka-Volterra food-chain model with time delays

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

Applied Mathematics

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

Abstract

A delayed three-species periodic Lotka-Volterra food-chain model without instantaneousnegative feedback is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness, and global stability of positive periodic solutions of the system. Computer simulations are presented to illustrate the conclusions.

Original language	English
Pages (from-to)	823-837
Number of pages	15
Journal	Mathematical and Computer Modelling
Volume	40
Issue number	7-8
DOIs	https://doi.org/10.1016/j.mcm.2004.10.011
Publication status	Published - 2004

Keywords

Food-chain model
Time delay
Periodic solution
Coincidence degree
Global stability

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10.1016/j.mcm.2004.10.011

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title = "Periodic solution for a three-species Lotka-Volterra food-chain model with time delays",

abstract = "A delayed three-species periodic Lotka-Volterra food-chain model without instantaneousnegative feedback is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness, and global stability of positive periodic solutions of the system. Computer simulations are presented to illustrate the conclusions.",

keywords = "Food-chain model, Time delay, Periodic solution, Coincidence degree, Global stability",

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

year = "2004",

doi = "10.1016/j.mcm.2004.10.011",

language = "English",

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journal = "Mathematical and Computer Modelling",

issn = "0895-7177",

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TY - JOUR

T1 - Periodic solution for a three-species Lotka-Volterra food-chain model with time delays

AU - Xu, Rui

AU - Chaplain, M. A. J.

AU - Davidson, F. A.

PY - 2004

Y1 - 2004

N2 - A delayed three-species periodic Lotka-Volterra food-chain model without instantaneousnegative feedback is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness, and global stability of positive periodic solutions of the system. Computer simulations are presented to illustrate the conclusions.

AB - A delayed three-species periodic Lotka-Volterra food-chain model without instantaneousnegative feedback is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness, and global stability of positive periodic solutions of the system. Computer simulations are presented to illustrate the conclusions.

KW - Food-chain model

KW - Time delay

KW - Periodic solution

KW - Coincidence degree

KW - Global stability

U2 - 10.1016/j.mcm.2004.10.011

DO - 10.1016/j.mcm.2004.10.011

M3 - Article

SN - 0895-7177

VL - 40

SP - 823

EP - 837

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

IS - 7-8

ER -

Periodic solution for a three-species Lotka-Volterra food-chain model with time delays

Abstract

Keywords

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