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

92 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

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Xiao, D., & Ruan, S. (2001). Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response. Journal of Differential Equations, 176(2), 494-510. https://doi.org/10.1006/jdeq.2000.3982

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