Direct observation of non-Markovian radiation dynamics in 3D bulk photonic crystals.

Since the very first proposition of photonic crystals, their influence on the dynamics of spontaneous emission has been of great interest. The radiation dynamics is described by an integration kernel which--in a spectral representation--comprises two equally important contributions: the Lamb shift and the radiative contribution to the linewidth. The latter is connected to the density of states via Fermi's golden rule.

Complete chaotic synchronization and exclusion of mutual Pyragas control in two delay-coupled Rössler-type oscillators.

Two identical chaotic oscillators that are mutually coupled via time delayed signals show very complex patterns of completely synchronized dynamics including stationary states and periodic as well as chaotic oscillations. We have experimentally observed these synchronized states in delay-coupled electronic circuits and have analyzed their stability by numerical simulations and analytical calculations. We found that the conditions for longitudinal and transversal stability largely exclude each other and prevent, e.

Experimental verification of Pyragas-Schöll-Fiedler control.

We present an experimental realization of time-delayed feedback control proposed by Schöll and Fiedler. The scheme enables us to stabilize torsion-free periodic orbits in autonomous systems, and to overcome the so-called odd number limitation. The experimental control performance is in quantitative agreement with the bifurcation analysis of simple model systems.

Stochastic modelling of intermittency.

Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics.

Noise-free stochastic resonance at an interior crisis.

We report on the observation of noise-free stochastic resonance in an externally driven diode resonator close to an interior crisis. At sufficiently high excitation amplitudes the diode resonator shows a strange attractor which after the collision with an unstable period-three orbit exhibits crisis-induced intermittency. In the intermittency regime the system jumps between the previously stable chaotic attractor and the phase space region which has been made accessible by the crisis.

Global properties in an experimental realization of time-delayed feedback control with an unstable control loop.

We demonstrate by electronic circuit experiments the feasibility of an unstable control loop to stabilize torsion-free orbits by time-delayed feedback control. Corresponding analytical normal form calculations and numerical simulations reveal a severe dependence of the basin of attraction on the particular coupling scheme of the control force. Such theoretical predictions are confirmed by the experiments and emphasize the importance of the coupling scheme for the global control performance.

Stochastic modeling of experimental chaotic time series.

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion.

Experimental relevance of global properties of time-delayed feedback control.

We show by means of theoretical considerations and electronic circuit experiments that time-delayed feedback control suffers from severe global constraints if transitions at the control boundaries are discontinuous. Subcritical behavior gives rise to small basins of attraction and thus limits the control performance. The reported properties are, on the one hand, universal since the mechanism is based on general arguments borrowed from bifurcation theory and, on the other hand, directly visible in experimental time series.

Theoretical and experimental aspects of chaos control by time-delayed feedback.

We review recent developments for the control of chaos by time-delayed feedback methods. While such methods are easily applied even in quite complex experimental context the theoretical analysis yields infinite-dimensional differential-difference systems which are hard to tackle. The essential ideas for a general theoretical approach are sketched and the results are compared to electronic circuits and to high power ferromagnetic resonance experiments.