Abstract and Applied Analysis

Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay

Chao Liu and Qingling Zhang

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 184174, 15 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278817

Digital Object Identifier
doi:10.1155/2014/184174

Mathematical Reviews number (MathSciNet)
MR3206772

Zentralblatt MATH identifier
07021891

Citation

Liu, Chao; Zhang, Qingling. Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 184174, 15 pages. doi:10.1155/2014/184174. https://projecteuclid.org/euclid.aaa/1412278817


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