Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response

Dongmei Xiao; Shigui Ruan

doi:10.1006/jdeq.2000.3982

Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response

Dongmei Xiao, Shigui Ruan

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

97 Scopus citations

Abstract

A delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by Faria and Magalhães. The bifurcation analysis of the model indicates that there is a Bogdanov-Takens singularity for any time delay value. A versal unfolding of the model at the Bogdanov-Takens singularity is obtained. On the other hand, it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit Hopf bifurcation as the time delay passes through some critical values.

Original language	English (US)
Pages (from-to)	494-510
Number of pages	17
Journal	Journal of Differential Equations
Volume	176
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.2000.3982
State	Published - Nov 1 2001
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1006/jdeq.2000.3982

Fingerprint Dive into the research topics of 'Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response'. Together they form a unique fingerprint.

Cite this

@article{453bd817d0654629bcfdc1d4c55b12a0,

title = "Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response",

abstract = "A delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by Faria and Magalh{\~a}es. The bifurcation analysis of the model indicates that there is a Bogdanov-Takens singularity for any time delay value. A versal unfolding of the model at the Bogdanov-Takens singularity is obtained. On the other hand, it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit Hopf bifurcation as the time delay passes through some critical values.",

author = "Dongmei Xiao and Shigui Ruan",

note = "Funding Information: 1Research supported by the National Natural Science Foundations of China. 2Research supported by the Natural Science and Engineering Research Council of Canada. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",

year = "2001",

month = nov,

day = "1",

doi = "10.1006/jdeq.2000.3982",

language = "English (US)",

volume = "176",

pages = "494--510",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response

AU - Xiao, Dongmei

AU - Ruan, Shigui

N1 - Funding Information: 1Research supported by the National Natural Science Foundations of China. 2Research supported by the Natural Science and Engineering Research Council of Canada. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2001/11/1

Y1 - 2001/11/1

N2 - A delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by Faria and Magalhães. The bifurcation analysis of the model indicates that there is a Bogdanov-Takens singularity for any time delay value. A versal unfolding of the model at the Bogdanov-Takens singularity is obtained. On the other hand, it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit Hopf bifurcation as the time delay passes through some critical values.

AB - A delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by Faria and Magalhães. The bifurcation analysis of the model indicates that there is a Bogdanov-Takens singularity for any time delay value. A versal unfolding of the model at the Bogdanov-Takens singularity is obtained. On the other hand, it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit Hopf bifurcation as the time delay passes through some critical values.

UR - http://www.scopus.com/inward/record.url?scp=0035507108&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035507108&partnerID=8YFLogxK

U2 - 10.1006/jdeq.2000.3982

DO - 10.1006/jdeq.2000.3982

M3 - Article

AN - SCOPUS:0035507108

VL - 176

SP - 494

EP - 510

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -

Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this