Stability and Hopf Bifurcation Analysis for a Stage-Structured Predator-Prey Model with Discrete and Distributed Delays
Joint Authors
Tang, Sanyi
Qi, Junmei
Shi, Ruiqing
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-03
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We propose a three-dimensional stage-structured predatory-prey model with discrete and distributed delays.
By use of a new variable, the original three-dimensional system transforms into an equivalent four-dimensional system.
Firstly, we study the existence and local stability of positive equilibrium of the new system.
And, by choosing the time delay τ as a bifurcation parameter, we show that Hopf bifurcation may occur as the time delay τ passes through some critical values.
Secondly, by use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation.
At last, some simple discussion is presented.
American Psychological Association (APA)
Shi, Ruiqing& Qi, Junmei& Tang, Sanyi. 2013. Stability and Hopf Bifurcation Analysis for a Stage-Structured Predator-Prey Model with Discrete and Distributed Delays. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-454048
Modern Language Association (MLA)
Shi, Ruiqing…[et al.]. Stability and Hopf Bifurcation Analysis for a Stage-Structured Predator-Prey Model with Discrete and Distributed Delays. Journal of Applied Mathematics No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-454048
American Medical Association (AMA)
Shi, Ruiqing& Qi, Junmei& Tang, Sanyi. Stability and Hopf Bifurcation Analysis for a Stage-Structured Predator-Prey Model with Discrete and Distributed Delays. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-454048
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-454048