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2014 Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay
Chao Liu, Qingling Zhang
Abstr. Appl. Anal. 2014(SI19): 1-15 (2014). DOI: 10.1155/2014/184174

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.

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Chao Liu. Qingling Zhang. "Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay." Abstr. Appl. Anal. 2014 (SI19) 1 - 15, 2014. https://doi.org/10.1155/2014/184174

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07021891
MathSciNet: MR3206772
Digital Object Identifier: 10.1155/2014/184174

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI19 • 2014
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