Hopf bifurcation analysis for a semiratio-dependent predator-prey system with two delays
type: Item
instance of: scholarly article
title: Hopf bifurcation analysis for a semiratio-dependent predator-prey system with two delays
zbMATH Open document ID: 1297.34094
DOI: 10.1155/2013/495072
author: Yanyan Li
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: This paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings.
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 34K19
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6306884
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: direction and stability
zbMATH Keywords: normal form method
zbMATH Keywords: center manifold theorem
Wikidata QID: Q58916896
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/495072
OpenAlex ID: W2121760860
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description: scientific article; zbMATH DE number 6306884