Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments

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

doi:10.1016/S1468-1218(03)00032-4

Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments

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

Applied Mathematics

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

Abstract

A delayed periodic Lotka?Volterra type predator-prey model with prey dispersal in two-patch environments 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 obtained to guarantee the existence, uniqueness and global stability of positive periodic solutions of the system. Numerical simulations are given to illustrate the feasibility of our main results.

Original language	English
Pages (from-to)	183-206
Number of pages	24
Journal	Nonlinear Analysis: Real World Applications
Volume	5
Issue number	1
DOIs	https://doi.org/10.1016/S1468-1218(03)00032-4
Publication status	Published - 2004

Keywords

Dispersion
Time delay
Periodic solution
Persistence
Global stability

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10.1016/S1468-1218(03)00032-4

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abstract = "A delayed periodic Lotka?Volterra type predator-prey model with prey dispersal in two-patch environments 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 obtained to guarantee the existence, uniqueness and global stability of positive periodic solutions of the system. Numerical simulations are given to illustrate the feasibility of our main results.",

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AU - Xu, Rui

AU - Chaplain, M. A. J.

AU - Davidson, F. A.

PY - 2004

Y1 - 2004

N2 - A delayed periodic Lotka?Volterra type predator-prey model with prey dispersal in two-patch environments 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 obtained to guarantee the existence, uniqueness and global stability of positive periodic solutions of the system. Numerical simulations are given to illustrate the feasibility of our main results.

AB - A delayed periodic Lotka?Volterra type predator-prey model with prey dispersal in two-patch environments 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 obtained to guarantee the existence, uniqueness and global stability of positive periodic solutions of the system. Numerical simulations are given to illustrate the feasibility of our main results.

KW - Dispersion

KW - Time delay

KW - Periodic solution

KW - Persistence

KW - Global stability

U2 - 10.1016/S1468-1218(03)00032-4

DO - 10.1016/S1468-1218(03)00032-4

M3 - Article

SN - 1468-1218

VL - 5

SP - 183

EP - 206

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 1

ER -

Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments

Abstract

Keywords

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