Control of unstable steady states by extended time-delayed feedback

Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This system represents a generic model of an unstable steady state which can be found for instance in a Hopf bifurcation. In addition to the original controller design, we investigate effects of control loop latency and a bandpass filter on the domain of control. Furthermore, we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase. We present an analysis of the domain of control and support our results by numerical calculations.Comment: 11 pages, 16 figure

Temperature and frequency dependent optical properties of ultra-thin Au films

While the optical properties of thin metal films are well understood in the visible and near-infrared range, little has been done in the mid- and far-infrared region. Here we investigate ultra-thin gold films prepared on Si(111)(7 x 7) in UHV by measuring in the frequency range between 500 cm-1 and 7000 cm-1 and for temperatures between 300 K and 5 K. The nominal thickness of the gold layers ranges between one monolayer and 9 nm. The frequency and temperature dependences of the thicker films can be well described by the Drude model of a metal, when taking into account classical size effects due to surface scattering. The films below the percolation threshold exhibit a non-metallic behavior: the reflection increases with frequency and decreases with temperature. The frequency dependence can partly be described by a generalized Drude model. The temperature dependence does not follow a simple activation process. For monolayers we observe a transition between surface states around 1100 cm-1.Comment: 7 pages, 10 figure

Control of unstable steady states by time-delayed feedback methods

We show that time-delayed feedback methods, which have successfully been used to control unstable periodic ortbits, provide a tool to stabilize unstable steady states. We present an analytical investigation of the feedback scheme using the Lambert function and discuss effects of both a low-pass filter included in the control loop and non-zero latency times associated with the generation and injection of the feedback signal.Comment: 8 pages, 11 figure

Tip-induced distortions in STM imaging of carbon nanotubes

By means of STM measurements and fully self-consistent transport calculations we analyze how STM trajectories for the mapping of nanostructures on surfaces are affected by the atomic structure of the tip. For the particular case of carbon nanotubes we show that considerable distortions of the STM trajectory with respect to the actual structure, position and diameter of the nanotube can occur for certain tip geometries. Comparison between theory and experiment can allow to characterize and correct these distortions

Adaptive Tuning of Feedback Gain in Time-Delayed Feedback Control

We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback gain. This adaptive controller is applied to the stabilization of an unstable fixed point and an unstable periodic orbit embedded in a chaotic attractor. The adaptation algorithm is constructed using the speed-gradient method of control theory. Our computer simulations show that the adaptation algorithm can find an appropriate value of the feedback gain for single and multiple delays. Furthermore, we show that our method is robust to noise and different initial conditions.Comment: 7 pages, 6 figure

Применение программного продукта Eclipse для оптимизации разработки нефтяных месторождений Западно-Сибирского региона

Применение программного продукта Eclipse для оптимизации разработки нефтяных месторождений Западно-Сибирского регионаApplication software Eclipse to optimize the development of oil fields of West Siberi

Coherence resonance in a network of FitzHugh-Nagumo systems: interplay of noise, time-delay and topology

We systematically investigate the phenomena of coherence resonance in time-delay coupled networks of FitzHugh-Nagumo elements in the excitable regime. Using numerical simulations, we examine the interplay of noise, time-delayed coupling and network topology in the generation of coherence resonance. In the deterministic case, we show that the delay-induced dynamics is independent of the number of nearest neighbors and the system size. In the presence of noise, we demonstrate the possibility of controlling coherence resonance by varying the time-delay and the number of nearest neighbors. For a locally coupled ring, we show that the time-delay weakens coherence resonance. For nonlocal coupling with appropriate time-delays, both enhancement and weakening of coherence resonance are possible

Controlling cluster synchronization by adapting the topology

We suggest an adaptive control scheme for the control of zero-lag and cluster synchronization in delay-coupled networks. Based on the speed-gradient method, our scheme adapts the topology of a network such that the target state is realized. It is robust towards different initial condition as well as changes in the coupling parameters. The emerging topology is characterized by a delicate interplay of excitatory and inhibitory links leading to the stabilization of the desired cluster state. As a crucial parameter determining this interplay we identify the delay time. Furthermore, we show how to construct networks such that they exhibit not only a given cluster state but also with a given oscillation frequency. We apply our method to coupled Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in an expansion of systems close to a Hopf bifurcation. The successful and robust control of this generic model opens up possible applications in a wide range of systems in physics, chemistry, technology, and life science

Excitability in autonomous Boolean networks

We demonstrate theoretically and experimentally that excitable systems can be built with autonomous Boolean networks. Their experimental implementation is realized with asynchronous logic gates on a reconfigurabe chip. When these excitable systems are assembled into time-delay networks, their dynamics display nanosecond time-scale spike synchronization patterns that are controllable in period and phase.Comment: 6 pages, 5 figures, accepted in Europhysics Letters (epljournal.edpsciences.org