scholarly journals Controlling spatio-temporal chaos in the scenario of the one-dimensional complex Ginzburg–Landau equation

2006 ◽  
Vol 364 (1846) ◽  
pp. 2383-2395 ◽  
Author(s):  
S Boccaletti ◽  
J Bragard
Keyword(s):  
Plane Wave ◽  
Landau Equation ◽  
Control Technique ◽  
Ginzburg Landau ◽  
Plane Wave Solution ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
System Extension ◽  
Spatio Temporal ◽  
The One

We discuss some issues related with the process of controlling space–time chaotic states in the one-dimensional complex Ginzburg–Landau equation. We address the problem of gathering control over turbulent regimes with the use of only a limited number of controllers, each one of them implementing, in parallel, a local control technique for restoring an unstable plane-wave solution. We show that the system extension does not influence the density of controllers needed in order to achieve control.

Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation

1992 ◽  
Vol 57 (3-4) ◽  
pp. 241-248 ◽  
Author(s):  
B.I. Shraiman ◽  
A. Pumir ◽  
W. van Saarloos ◽  
P.C. Hohenberg ◽  
H. Chaté ◽  
...  
Keyword(s):  
Landau Equation ◽  
Spatiotemporal Chaos ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

scholarly journals Studies of phase turbulence in the one-dimensional complex Ginzburg-Landau equation

1997 ◽  
Vol 55 (5) ◽  
pp. 5073-5081 ◽  
Author(s):  
Alessandro Torcini ◽  
Helge Frauenkron ◽  
Peter Grassberger
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

Stable Stationary Solitons of the One-Dimensional Modified Complex Ginzburg-Landau Equation

2007 ◽  
Vol 62 (7-8) ◽  
pp. 368-372
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Landau Equation ◽  
Model Parameters ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Paraxial Ray Approximation ◽  
New Family ◽  
Ginzburg Landau Equation ◽  
The Stability ◽  
The One ◽  
Paraxial Ray

We report on the existence of a new family of stable stationary solitons of the one-dimensional modified complex Ginzburg-Landau equation. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons.

scholarly journals A variational formulation for translation and assimilation of coherent structures

2013 ◽  
Vol 20 (5) ◽  
pp. 793-801
Author(s):  
M. Plu
Keyword(s):  
Dynamical System ◽  
Data Assimilation ◽  
Coherent Structures ◽  
Variational Formulation ◽  
Landau Equation ◽  
Variational Data Assimilation ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

Abstract. The assimilation of observations from teledetected images in geophysical models requires one to develop algorithms that would account for the existence of coherent structures. In the context of variational data assimilation, a method is proposed to allow the background to be translated so as to fit structure positions deduced from images. Translation occurs as a first step before assimilating all the observations using a classical assimilation procedure with specific covariances for the translated background. A simple validation is proposed using a dynamical system based on the one-dimensional complex Ginzburg–Landau equation in a regime prone to phase and amplitude errors. Assimilation of observations after background translation leads to better scores and a better representation of extremas than the method without translation.

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