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Standing waves in a complex Ginzburg-Landau equation with time-delay feedback

Pages: 1329 - 1334, Issue Special, September 2011

 Abstract        Full Text (114.5K)              

Michael Stich - Centro de Astrobiología (CSIC-INTA), Ctra. de Ajalvir, km. 4, 28850 Torrejón de Ardoz (Madrid), Spain (email)
Carsten Beta - Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, Haus 28, 14476 Potsdam, Germany (email)

Abstract: Standing waves are studied as solutions of a complex Ginzburg- Landau equation subjected to local and global time-delay feedback terms. The onset of standing waves is studied at the instability of the homogeneous periodic solution with respect to spatially periodic perturbations. The solution of this spatiotemporal wave pattern is given and is compared to the homogeneous periodic solution.

Keywords:  pattern formation, reaction-diffusion system, control
Mathematics Subject Classification:  Primary: 35K57; 35B10; Secondary: 35Q92

Received: August 2010;      Revised: April 2011;      Published: October 2011.