Controlling spatiotemporal dynamics with time-delay feedback

We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external generation of an ideal reference state and can suppress both absolute and convective instabilities. As an example, we analyze the complex Ginzburg-Landau equation in one dimension, showing how the time-delay feedback enlarges the stability domain for travelling waves.Comment: 4 pages REVTeX + postscript file with 3 figure

Controlling extended systems with spatially filtered, time-delayed feedback

We investigate a control technique for spatially extended systems combining spatial filtering with a previously studied form of time-delay feedback. The scheme is naturally suited to real-time control of optical systems. We apply the control scheme to a model of a transversely extended semiconductor laser in which a desirable, coherent traveling wave state exists, but is a member of a nowhere stable family. Our scheme stabilizes this state, and directs the system towards it from realistic, distant and noisy initial conditions. As confirmed by numerical simulation, a linear stability analysis about the controlled state accurately predicts when the scheme is successful, and illustrates some key features of the control including the individual merit of, and interplay between, the spatial and temporal degrees of freedom in the control.Comment: 9 pages REVTeX including 7 PostScript figures. To appear in Physical Review

Stability domains for time-delay feedback control with latency

We generalize a known analytical method for determining the stability of periodic orbits controlled by time-delay feedback methods when latencies associated with the generation and injection of the feedback signal cannot be ignored. We discuss the case of extended time-delay autosynchronization (ETDAS) and show that nontrivial qualitative features of the domain of control observed in experiments can be explained by taking into account the effects of both the unstable eigenmode and a single stable eigenmode in the Floquet theory.Comment: 9 pages, 6 figures; Submitted to Physical Review

The critical properties of the agent-based model with environmental-economic interactions

The steady-state and nonequilibrium properties of the model of environmental-economic interactions are studied. The interacting heterogeneous agents are simulated on the platform of the emission dynamics of cellular automaton. The model possess the discontinuous transition between the safe and catastrophic ecology. Right at the critical line, the broad-scale power-law distributions of emission rates have been identified. Their relationship to Zipf's law and models of self-organized criticality is discussed.Comment: 12 pages, 6 figures, published in Physica

Time-delayed feedback control in astrodynamics

In this paper we present time-delayed feedback control (TDFC) for the purpose of autonomously driving trajectories of nonlinear systems into periodic orbits. As the generation of periodic orbits is a major component of many problems in astodynamics we propose this method as a useful tool in such applications. To motivate the use of this method we apply it to a number of well known problems in the astrodynamics literature. Firstly, TDFC is applied to control in the chaotic attitude motion of an asymmetric satellite in an elliptical orbit. Secondly, we apply TDFC to the problem of maintaining a spacecraft in a periodic orbit about a body with large ellipticity (such as an asteroid) and finally, we apply TDFC to eliminate the drift between two satellites in low Earth orbits to ensure their relative motion is bounded

On the Mechanism of Time--Delayed Feedback Control

The Pyragas method for controlling chaos is investigated in detail from the experimental as well as theoretical point of view. We show by an analytical stability analysis that the revolution around an unstable periodic orbit governs the success of the control scheme. Our predictions concerning the transient behaviour of the control signal are confirmed by numerical simulations and an electronic circuit experiment.Comment: 4 pages, REVTeX, 4 eps-figures included Phys. Rev. Lett., in press also available at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.htm

Establishment of a guided, in vivo, multi-channel, abdominal, tissue imaging approach

Novel tools in humane animal research should benefit the animal as well as the experimentally obtained data. Imaging technologies have proven to be versatile and also in accordance with the demands of the 3 R principle. However, most imaging technologies are either limited by the target organs, number of repetitive imaging sessions, or the maximal resolution. We present a technique-, which enables multicolor abdominal imaging on a tissue level. It is based on a small imaging fiber endoscope, which is guided by a second commercial endoscope. The imaging fiber endoscope allows the distinction of four different fluorescence channels. It has a size of less than 1 mm and can approximately resolve single cells. The imaging fiber was successfully tested on cells in vitro, excised organ tissue, and in mice in vivo. Combined with neural networks for image restauration, high quality images from various abdominal organs of interest were realized. The second endoscope ensured a precise placement of the imaging fiber in vivo. Our approach of guided tissue imaging in vivo, combined with neuronal networks for image restauration, permits the acquisition of fluorescence-microscope like images with minimal invasive surgery in vivo. Therefore, it is possible to extend our approach to repetitive imaging sessions. The cost below 30 thousand euros allows an establishment of this approach in various scenarios. © 2020, The Author(s)