O(2)O(2)-Hopf bifurcation for a model of cellular shock instability

We study by center manifold and normal form reduction an O(2)O(2)-Hopf bifurcation arising in a simplified model of bifurcating viscous shock waves in a channel, suppressing longitudinal dependence and modeling onset of instability via competing stable/unstable diffusions. For this canonical system,...

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Bibliographic Details
Published in:Physica. D 2014-02, Vol.269, p.63-75
Main Author: Yao, Jinghua
Format: Article
Language:English
Subjects:
Bifurcations
Cellular
Channels
Diffusion
Instability
Manifolds
Retarding
Stability
Online Access:Get full text
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Summary:We study by center manifold and normal form reduction an O(2)O(2)-Hopf bifurcation arising in a simplified model of bifurcating viscous shock waves in a channel, suppressing longitudinal dependence and modeling onset of instability via competing stable/unstable diffusions. For this canonical system, a cousin of the Kuramoto-Sivashinsky model, we are able to carry out a complete bifurcation analysis.
ISSN:0167-2789
DOI:10.1016/j.physd.2013.11.005