Hopf bifurcation in numerical approximation of the sunflower equation
type: Item
instance of: scholarly article
title: Hopf bifurcation in numerical approximation of the sunflower equation
zbMATH Open document ID: 1111.65064
DOI: 10.1007/BF02896464
author: Baodong Zheng
author: Chunrui Zhang
published in: Journal of Applied Mathematics and Computing
publication date: 2006-12-04T00:00:00Z
review text: Initial value problems of the sunflower equation are considered, which represents a scalar delay differential equation of second order. The analysis is based on an equivalent system of two ordinary differential equations (ODEs) of first order with delay. Hopf bifurcation arises for a specific class of parameters. The authors consider the explicit Euler method to obtain a numerical approximation of an initial value problem. The resulting difference equations are analysed in detail. Assuming a Hopf bifurcation at some parameter in the system of ODEs, the authors prove that the corresponding system of difference equations exhibits a Hopf bifurcation for sufficiently small step sizes, too. The difference between both bifurcation points decreases linearly in dependence on the step size applied in the Euler method. Moreover, a proof is given that the direction and stability properties of the two Hopf bifurcations coincide for sufficiently small step sizes.
reviewed by: Roland Pulch
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K28
zbMATH DE Number: 5076938
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: sunflower equation
zbMATH Keywords: delay differential equation
zbMATH Keywords: Euler method
zbMATH Keywords: stability
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02896464
OpenAlex ID: W1972448501
description: scientific article; zbMATH DE number 5076938