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Time-delayed feedback control of noise-induced patterns in semiconductors

A central point of our Subdivision is the application of time-delayed feedback control to noise-induced spatio-temporal patterns in reaction-diffusion systems. We have extended the globally coupled  reaction-diffusion system, which describes a resonant tunneling diode, by adding Gaussian white noise and a feedback loop in the circuit.

In the absence of noise and delay, the system exhibits a Hopf bifurcation, by which a stable spatially inhomogeneous filamentary fixed point changes into a breathing current filament. Preparing the system below the Hopf bifurcation, noise-induced  breathing filamentary patterns can be orserved, the temporal coherence of which decreases with increasing noise intensity, whereas the spatial homogenity increases. The coherence of these localized oscillatory patterns can be drastically improved by time-delayed feedback with suitable time delays, although the control force is acting only on the spatially homogeneous voltage variable. For other values of the time delay, the coherence is substantially decreased. Through an extensive analytical linear mode analysis of the inhomogeneous fixed point, we succeeded in explaining this behaviour in detail. The eigenvalue spectrum actually behaves similarly as in the simple models, and we therefore have identified a universal mechanism of time-delayed feedbak control in the vicinity of a Hopf bifurcation in a spatially inhomogeneous medium as well.

In collaboration with Subdivision B6 we have applied time-delayed feedback control to noise-induced travelling pulses in a local reaction-diffusion system. We found a significant variation, with the time delay, of the spatial and temporal correlation, as well as of the mean interspike interval and its normalized variance (as measure for coherence), in a 3-variable Oregonator model describing the light-sensitive Belousov-Zhabotinski reaction.

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