The Hopf bifurcation for a predator-prey system with \(\theta\)-logistic growth and prey refuge
type: Item
instance of: scholarly article
title: The Hopf bifurcation for a predator-prey system with \(\theta\)-logistic growth and prey refuge
zbMATH Open document ID: 1303.34067
DOI: 10.1155/2013/168340
author: Shaoli Wang
author: Zhihao Ge
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: The Hopf bifurcation for a predator-prey system with \(\theta\)-logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index-\(\theta\) passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K19
zbMATH DE Number: 6306087
zbMATH Keywords: positive equilibrium
zbMATH Keywords: normal form theory
zbMATH Keywords: center manifold reduction
Wikidata QID: Q58915418
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/168340
OpenAlex ID: W2010429899
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description: scientific article; zbMATH DE number 6306087