Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays

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

doi:10.1016/S0096-3003(02)00918-9

Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays

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

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

32 Citations (Scopus)

Abstract

A periodic Lotka–Volterra predator–prey model with dispersion and time delays is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and by means of 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. Sufficient conditions are also established for the uniform persistence of the system. Numerical simulations are presented to illustrate our main results.

Original language	English
Pages (from-to)	537-560
Number of pages	24
Journal	Applied Mathematics and Computation
Volume	148
Issue number	2
DOIs	https://doi.org/10.1016/S0096-3003(02)00918-9
Publication status	Published - 2004

Keywords

Dispersion
Time delay
Periodic solution
Persistence
Global stability

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10.1016/S0096-3003(02)00918-9

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title = "Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays",

abstract = "A periodic Lotka–Volterra predator–prey model with dispersion and time delays is investigated. By using Gaines and Mawhin{\textquoteright}s continuation theorem of coincidence degree theory and by means of 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. Sufficient conditions are also established for the uniform persistence of the system. Numerical simulations are presented to illustrate our main results.",

keywords = "Dispersion, Time delay, Periodic solution, Persistence, Global stability",

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T1 - Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays

AU - Xu, R.

AU - Chaplain, M. A. J.

AU - Davidson, F. A.

N1 - dc.publisher: Elsevier

PY - 2004

Y1 - 2004

N2 - A periodic Lotka–Volterra predator–prey model with dispersion and time delays is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and by means of 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. Sufficient conditions are also established for the uniform persistence of the system. Numerical simulations are presented to illustrate our main results.

AB - A periodic Lotka–Volterra predator–prey model with dispersion and time delays is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and by means of 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. Sufficient conditions are also established for the uniform persistence of the system. Numerical simulations are presented to illustrate our main results.

KW - Dispersion

KW - Time delay

KW - Periodic solution

KW - Persistence

KW - Global stability

U2 - 10.1016/S0096-3003(02)00918-9

DO - 10.1016/S0096-3003(02)00918-9

M3 - Article

SN - 0096-3003

VL - 148

SP - 537

EP - 560

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays

Abstract

Keywords

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