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

Dongmei Xiao, Shigui Ruan

Research output: Contribution to journalArticle

88 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)494-510
Number of pages17
JournalJournal of Differential Equations
Volume176
Issue number2
DOIs
StatePublished - Nov 1 2001
Externally publishedYes

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Predator prey systems
Functional Response
Predator-prey System
Bifurcation
Time Delay
Time delay
Singularity
Retarded Functional Differential Equations
Normal Form Theory
Hopf bifurcation
Bifurcation Analysis
Unfolding
Hopf Bifurcation
Critical value
Differential equations
Model

ASJC Scopus subject areas

  • Analysis

Cite this

Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response. / Xiao, Dongmei; Ruan, Shigui.

In: Journal of Differential Equations, Vol. 176, No. 2, 01.11.2001, p. 494-510.

Research output: Contribution to journalArticle

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