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Instabilities and Dynamics of Weakly SubcriticalPatterns

Published online by Cambridge University Press:  17 September 2013

H.-C Kao  and
E. Knobloch
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Abstract

The bifurcation to one-dimensional weakly subcritical periodic patterns is described bythe cubic-quintic Ginzburg-Landau equation

       At = µA + Axx + i(a1|A|2Ax + a2A2Ax*) + b|A|2A - |A|4A.

These periodic patterns may in turn become unstable through one of two differentmechanisms, an Eckhaus instability or an oscillatory instability. We study the dynamicsnear the instability threshold in each of these cases using the corresponding modulationequations and compare the results with those obtained from direct numerical simulation ofthe equation. We also study the stability properties and dynamical evolution of differenttypes of fronts present in the protosnaking region of this equation. The results providenew predictions for the dynamical properties of generic systems in the weakly subcriticalregime.

Keywords

bifurcationcubic-quintic Ginzburg-Landau equationweakly subcritical periodic pattern
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 5: Bifurcations , 2013 , pp. 131 - 154
Copyright
© EDP Sciences, 2013

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