Dynamics of a modified predator-prey system to allow for a functional response and time delay

Wei Liu; Yaolin Jiang

doi:10.4208/eajam.141214.050616a

Dynamics of a modified predator-prey system to allow for a functional response and time delay

Wei Liu
, Yaolin Jiang

School of Mathematics and Statistics

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

5 Scopus citations

Abstract

A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differentialalgebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

Original language	English
Pages (from-to)	384-399
Number of pages	16
Journal	East Asian Journal on Applied Mathematics
Volume	6
Issue number	4
DOIs	https://doi.org/10.4208/eajam.141214.050616a
State	Published - 1 Nov 2016

Keywords

Harvesting
Periodic solutions
Predator-prey system
Stability
Time delay

Access to Document

10.4208/eajam.141214.050616a

Cite this

@article{68587ad86c5648ad8ce7d60e1f4f9060,

title = "Dynamics of a modified predator-prey system to allow for a functional response and time delay",

abstract = "A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differentialalgebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.",

keywords = "Harvesting, Periodic solutions, Predator-prey system, Stability, Time delay",

author = "Wei Liu and Yaolin Jiang",

note = "Publisher Copyright: {\textcopyright} 2016 Global-Science Press.",

year = "2016",

month = nov,

day = "1",

doi = "10.4208/eajam.141214.050616a",

language = "英语",

volume = "6",

pages = "384--399",

journal = "East Asian Journal on Applied Mathematics",

issn = "2079-7362",

publisher = "Global Science Press",

number = "4",

}

TY - JOUR

T1 - Dynamics of a modified predator-prey system to allow for a functional response and time delay

AU - Liu, Wei

AU - Jiang, Yaolin

PY - 2016/11/1

Y1 - 2016/11/1

N2 - A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differentialalgebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

AB - A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differentialalgebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

KW - Harvesting

KW - Periodic solutions

KW - Predator-prey system

KW - Stability

KW - Time delay

UR - https://www.scopus.com/pages/publications/84994055994

U2 - 10.4208/eajam.141214.050616a

DO - 10.4208/eajam.141214.050616a

M3 - 文章

AN - SCOPUS:84994055994

SN - 2079-7362

VL - 6

SP - 384

EP - 399

JO - East Asian Journal on Applied Mathematics

JF - East Asian Journal on Applied Mathematics

IS - 4

ER -

Dynamics of a modified predator-prey system to allow for a functional response and time delay

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this