Control of pattern formation by time-delay feedback with global and local contributions |
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Authors: | Michael Stich Carsten Beta |
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Institution: | a Centro de Astrobiología (CSIC-INTA), Ctra de Ajalvir km 4, 28850 Torrejón de Ardoz (Madrid), Spain b Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, Haus 28, D-14476 Potsdam, Germany |
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Abstract: | We consider the suppression of spatiotemporal chaos in the complex Ginzburg-Landau equation by a combined global and local time-delay feedback. Feedback terms are implemented as a control scheme, i.e., they are proportional to the difference between the time-delayed state of the system and its current state. We perform a linear stability analysis of uniform oscillations with respect to space-dependent perturbations and compare with numerical simulations. Similarly, for the fixed-point solution that corresponds to amplitude death in the spatially extended system, a linear stability analysis with respect to space-dependent perturbations is performed and complemented by numerical simulations. |
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Keywords: | Pattern formation Reaction-diffusion systems Chaos control Feedback |
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