![](/images/graphics-bg.png)
Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-27
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We propose a prey predator model with stage structure for prey.
A discrete delay and a distributed delay for predator described by an integral with a strong delay kernel are also considered.
Existence of two feasible boundary equilibria and a unique interior equilibrium are analytically investigated.
By analyzing associated characteristic equation, local stability analysis of boundary equilibrium and interior equilibrium is discussed, respectively.
It reveals that interior equilibrium is locally stable when discrete delay is less than a critical value.
According to Hopf bifurcation theorem for functional differential equations, it can be found that model undergoes Hopf bifurcation around the interior equilibrium when local stability switch occurs and corresponding stable limit cycle is observed.
Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied based on normal form theory and center manifold theorem.
Numerical simulations are carried out to show consistency with theoretical analysis.
American Psychological Association (APA)
Liu, Chao& Zhang, Qing-ling. 2014. Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-1013437
Modern Language Association (MLA)
Liu, Chao& Zhang, Qing-ling. Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay. Abstract and Applied Analysis No. 2014 (2014), pp.1-15.
https://search.emarefa.net/detail/BIM-1013437
American Medical Association (AMA)
Liu, Chao& Zhang, Qing-ling. Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-1013437
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013437