Periodic solutions of a Lotka-Volterra type multi-species population model with time delays

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

doi:10.1002/mana.200310402

Periodic solutions of a Lotka-Volterra type multi-species population model with time delays

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

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

Abstract

A delayed periodic Lotka-Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulation is presented to illustrate the feasibility of our main results.

Original language	English
Pages (from-to)	911-927
Number of pages	17
Journal	Mathematische Nachrichten
Volume	279
Issue number	8
DOIs	https://doi.org/10.1002/mana.200310402
Publication status	Published - 2006

Keywords

Periodic solution
Lyapunov functional
Global stability
Time delay

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10.1002/mana.200310402

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title = "Periodic solutions of a Lotka-Volterra type multi-species population model with time delays",

abstract = "A delayed periodic Lotka-Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulation is presented to illustrate the feasibility of our main results.",

keywords = "Periodic solution, Lyapunov functional, Global stability, Time delay",

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

note = "dc.publisher: John Wiley & Sons ",

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journal = "Mathematische Nachrichten",

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AU - Xu, Rui

AU - Chaplain, M. A. J.

AU - Davidson, F. A.

N1 - dc.publisher: John Wiley & Sons

PY - 2006

Y1 - 2006

N2 - A delayed periodic Lotka-Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulation is presented to illustrate the feasibility of our main results.

AB - A delayed periodic Lotka-Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulation is presented to illustrate the feasibility of our main results.

KW - Periodic solution

KW - Lyapunov functional

KW - Global stability

KW - Time delay

U2 - 10.1002/mana.200310402

DO - 10.1002/mana.200310402

M3 - Article

SN - 0025-584X

VL - 279

SP - 911

EP - 927

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 8

ER -

Periodic solutions of a Lotka-Volterra type multi-species population model with time delays

Abstract

Keywords

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