Periodic solutions for a predator-prey model with Holling-type functional response and time delays

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

doi:10.1016/j.amc.2003.12.054

Periodic solutions for a predator-prey model with Holling-type functional response and time delays

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

Applied Mathematics

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

Abstract

A delayed periodic Holling-type predator?prey model without instantaneous negative feedback is investigated. By using the continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions to the model. Numerical simulation is carried out to illustrate the feasibility of our main results.

Original language	English
Pages (from-to)	637-654
Number of pages	18
Journal	Applied Mathematics and Computation
Volume	161
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2003.12.054
Publication status	Published - 2005

Keywords

Predator-prey system
Time delay
Periodic solution
Lyapunov functional
Global stability

Access to Document

10.1016/j.amc.2003.12.054

Cite this

@article{4cd414d358034f5baea4085c509bd297,

title = "Periodic solutions for a predator-prey model with Holling-type functional response and time delays",

abstract = "A delayed periodic Holling-type predator?prey model without instantaneous negative feedback is investigated. By using the continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions to the model. Numerical simulation is carried out to illustrate the feasibility of our main results.",

keywords = "Predator-prey system, Time delay, Periodic solution, Lyapunov functional, Global stability",

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

year = "2005",

doi = "10.1016/j.amc.2003.12.054",

language = "English",

volume = "161",

pages = "637--654",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

number = "2",

}

TY - JOUR

T1 - Periodic solutions for a predator-prey model with Holling-type functional response and time delays

AU - Xu, Rui

AU - Chaplain, M. A. J.

AU - Davidson, F. A.

PY - 2005

Y1 - 2005

N2 - A delayed periodic Holling-type predator?prey model without instantaneous negative feedback is investigated. By using the continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions to the model. Numerical simulation is carried out to illustrate the feasibility of our main results.

AB - A delayed periodic Holling-type predator?prey model without instantaneous negative feedback is investigated. By using the continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions to the model. Numerical simulation is carried out to illustrate the feasibility of our main results.

KW - Predator-prey system

KW - Time delay

KW - Periodic solution

KW - Lyapunov functional

KW - Global stability

U2 - 10.1016/j.amc.2003.12.054

DO - 10.1016/j.amc.2003.12.054

M3 - Article

SN - 0096-3003

VL - 161

SP - 637

EP - 654

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Periodic solutions for a predator-prey model with Holling-type functional response and time delays

Abstract

Keywords

Access to Document

Fingerprint

Cite this