Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Poster II
DY 26.13: Poster
Thursday, March 26, 2009, 16:00–18:00, P1A
Time-delayed control of spatio-temporal chaos in the Gray-Scott model — Yuliya N. Kyrychko1, Konstantin B. Blyuss1, and •Eckehard Schöll2 — 1Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR, UK — 2Institut f. Theo. Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
Effects of time-delayed feedback control on the dynamics of spatio-temporal patterns in the Gray-Scott reaction-diffusion system are studied numerically. Several kinds of control schemes are investigated, including single-species, diagonal and mixed control. In the case of spatio-temporal chaos, the control may stabilize uniform steady states or lead to bistability between a trivial steady state and a propagating travelling wave. When the basic state is a stable travelling pulse, the control can provide either a stationary Turing pattern, or the above-mentioned bistability. In each case, the stability boundary is found in the parameter space of the control strength and the time delay. Numerical simulations suggest that diagonal control fails to stabilize spatio-temporal chaos.