Bifurcation analysis of delay-induced periodic oscillations
type: Item
instance of: scholarly article
title: Bifurcation analysis of delay-induced periodic oscillations
zbMATH Open document ID: 1201.34105
author: N. E. Zubov
published in: Journal of Computational and Applied Mathematics
publication date: 2010-02-12T00:00:00Z
review text: The paper provides a detailed numerical bifurcation analysis of the following system with time-delay and cubic nonlinearity \[ \frac{dz}{dt} = (\alpha + i \beta) z -z|z|^2 +z(t-\tau), \] where \(z(t)\) is a complex variable and \(\alpha\) and \(\beta\) are real parameters. As shown in [\textit{M. Wolfrum} and \textit{S. Yanchuk}, Phys. Rev. Lett. 96, 220201 (1997)] this system undergoes oscillatory (Eckhaus) instability with a number of periodic solutions appearing as the parameter \(\alpha\) increases over \(-1\). The present research uses the DDE-Biftool software [see \textit{D. Roose, T. Luzyanina, K. Engelborghs} and \textit{W. Michiels}, Lecture Notes in Computational Science and Engineering 38, 167--181 (2004; Zbl 1065.34077)] and investigates the bifurcation mechanisms behind this.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 65P30
zbMATH DE Number: 5669165
zbMATH Keywords: Eckhaus instability
zbMATH Keywords: periodic solutions
zbMATH Keywords: codimension-two bifurcations
zbMATH Keywords: delay
describes a project that uses: DDE-BIFTOOL
MaRDI profile type: Publication
full work available at URL: j.cam.2009.10.025
OpenAlex ID: W1970522247
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DOI: 10.1016/J.CAM.2009.10.025
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description: scientific article; zbMATH DE number 5669165