American Institute of Mathematical Sciences

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2011, 2011(Special): 1329-1334. doi: 10.3934/proc.2011.2011.1329

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

Michael Stich 1, and  Carsten Beta 2,

1. 

Centro de Astrobiología (CSIC-INTA), Ctra. de Ajalvir, km. 4, 28850 Torrejón de Ardoz (Madrid), Spain
2. 

Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, Haus 28, 14476 Potsdam, Germany

Received  August 2010 Revised  April 2011 Published  October 2011

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: reaction-diffusion system, control, pattern formation.
Mathematics Subject Classification: Primary: 35K57; 35B10; Secondary: 35Q92.
Citation: Michael Stich, Carsten Beta. Standing waves in a complex Ginzburg-Landau equation with time-delay feedback. Conference Publications, 2011, 2011 (Special) : 1329-1334. doi: 10.3934/proc.2011.2011.1329
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