Bifurcation analysis in single-species population model with delay
type: Item
instance of: scholarly article
title: Bifurcation analysis in single-species population model with delay
zbMATH Open document ID: 1195.34127
published in: Science China. Mathematics
publication date: 2010-08-23T00:00:00Z
review text: The authors consider the scalar differential-delay equation \[ {dN(t)\over dt}= be^{-aN(t-\tau)}N(t-\tau) e^{-d_1\tau}- dN(t) \] under the conditions \(a> 0\), \(d>0\), \(d_1\geq 0\), \(b> de^{d_1\tau+ 2}\), \(\tau\geq 0\). They study the stability of the positive equilibrium \(N= N^4= {1\over a}\ln{b\over de^{d_1\tau}}\) and prove the occurrence of Hopf bifurcation with \(\tau\) as bifurcation parameter. The direction of Hopf bifurcation is also determined.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5774152
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: stability
zbMATH Keywords: time delay
zbMATH Keywords: numerical simulations
author: Zhichao Jiang
author: Wenzhi Zhang
MaRDI profile type: Publication
full work available at URL: s11425-010-4008-5
OpenAlex ID: W2169535042
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DOI: 10.1007/S11425-010-4008-5
description: scientific article; zbMATH DE number 5774152