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

Advances in the analysis of short span railway bridges for high-speed lines

The physical model based on moving constant loads is widely used for the analysis of railway bridges. Nevertheless, the moving loads model is not well suited for the study of short bridges (L⩽20–25 m) since the results it produces (displacements and accelerations) are much greater than those obtained from more sophisticated ones. In this paper two factors are analysed which are believed to have an influence in the dynamic behaviour of short bridges. These two factors are not accounted for by the moving loads model and are the following: the distribution of the loads due to the presence of the sleepers and ballast layer, and the train–bridge interaction. In order to decide on their influence several numerical simulations have been performed. The results are presented and discussed herein