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Taming turbulence in the complex Ginzburg-Landau equation.

Authors
  • Zhan, Meng
  • Zou, Wei
  • Liu, Xu
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society (APS)
Publication Date
Mar 01, 2010
Volume
81
Issue
3 Pt 2
Pages
36211–36211
Identifiers
PMID: 20365836
Source
Medline
License
Unknown

Abstract

Taming turbulence in the complex Ginzburg-Landau equation (CGLE) by using a global feedback control method and choosing traveling-wave solutions as our target state is investigated. The problem of optimal control for the smallest driving strength is studied by systematically comparing the stabilities of all traveling waves. Within the Benjamin-Feir-Newell unstable parameter region (c2<-c1 -1, a critical control curve is determined, which is located at c2=alphacbeta1 , with alpha approximately -4.0 and beta approximately -0.87. It characterizes the transition of chosen traveling-wave target state from long wavelength to short one. This finding is of great significance for taming turbulence in the CGLE and some other spatiotemporal systems as well.

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