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 | |
| State | Published - Nov 1 2001 |
| Externally published | Yes |
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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 journal › Article
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TY - JOUR
T1 - Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response
AU - Xiao, Dongmei
AU - Ruan, Shigui
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 -