Dynamical behavior and stability analysis in a stage-structured prey predator model with discrete delay and distributed delay
type: Item
instance of: scholarly article
title: Dynamical behavior and stability analysis in a stage-structured prey predator model with discrete delay and distributed delay
zbMATH Open document ID: 1468.34113
DOI: 10.1155/2014/184174
author: Chao Liu
author: Qingling Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 7021891
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/184174
OpenAlex ID: W2159799263
Wikidata QID: Q59035857
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description: scientific article; zbMATH DE number 7021891