Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators

We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.Comment: postprint, as accepted in Chaos, 10 pages, 7 figure

Temporal dissipative solitons in time-delay feedback systems

Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, auto-solitons, spot or pulse solutions, these states play an important role in data transmission using optical pulses, neural signal propagation, and other processes. While this phenomenon was thoroughly studied in spatially extended systems, temporally localized states are gaining attention only recently, driven primarily by applications from fiber or semiconductor lasers. Here we present a theory for temporal dissipative solitons (TDS) in systems with time-delayed feedback. In particular, we derive a system with an advanced argument, which determines the profile of the TDS. We also provide a complete classification of the spectrum of TDS into interface and pseudo-continuous spectrum. We illustrate our theory with two examples: a generic delayed phase oscillator, which is a reduced model for an injected laser with feedback, and the FitzHugh-Nagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudo-continuous spectrum develops a modulational instability.Comment: 5 pages, 4 figures, submitted (revision) supplementary material available at https://doi.org/10.6084/m9.figshare.8269757 source code for reproducing figures 1a,b, 2a, 3a,b,c available at https://doi.org/10.6084/m9.figshare.824167

Impact of gain dispersion on the spatio-temporal dynamics of multisection lasers

We present a refined model for multi-section lasers, introducing an additional equation for material polarization in the well known travelling wave model. We investigate the polarization-induced changes in the spectral properties of the optical waveguide. Finally, we show the relevance of this model for a more realistic simulation of complicated dynamical behaviour of multi-section Distributed Feedback (DFB)-Lasers, such as fast self-pulsations, multi-stability, and hysteresis effects due to mode competition

Temporal dissipative solitons in time-delay feedback systems

Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, auto-solitons, spot or pulse solitons, these states play an important role in data transmission using optical pulses, neural signal propagation, and other processes. While this phenomenon was thoroughly studied in spatially extended systems, temporally localized states are gaining attention only recently, driven primarily by applications from fiber or semiconductor lasers. Here we present a theory for temporal dissipative solitons (TDS) in systems with time-delayed feedback. In particular, we derive a system with an advanced argument, which determines the profile of the TDS. We also provide a complete classification of the spectrum of TDS into interface and pseudo-continuous spectrum. We illustrate our theory with two examples: a generic delayed phase oscillator, which is a reduced model for an injected laser with feedback, and the FitzHugh--Nagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudo-continuous spectrum develops a modulational instability

Controlling unstable chaos: stabilizing chimera states by feedback

Copyright © 2014 American Physical SocietyWe present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it loses its attractivity. Similar to classical delayed feedback control, the scheme is noninvasive, however only in an appropriately relaxed sense considering the chaotic regime as a statistical equilibrium displaying random fluctuations as a finite size effect. We demonstrate the control scheme for so-called chimera states, which are coherence-incoherence patterns in coupled oscillator systems. The control makes chimera states observable close to coherence, for small numbers of oscillators, and for random initial conditions.Engineering and Physical Sciences Research Council (EPSRC

Cadmium isotope fractionation in an intertidal soil induced by tidal pumping

Estuarine floodplain soils are both sinks and potential sources of toxic trace metals such as Cd. Mobilization of Cd has been identified through spatiotemporal monitoring in intertidal sediments during the last decades, but no information was yet available as to what extent these biogeochemical dynamics change the Cd isotopic composition. Cores of an Aquic Udifluvent soil from an intertidal mudflat of the Elbe River, Germany, were sub-sampled at 2 cm intervals to a depth of 40 cm corresponding to a sedimentation of about 10 years. Strong redox zonation was found in the cores, with an upper suboxic zone and a lower anoxic zone of significantly different Cd isotopy. Cadmium partitioning and pore water data determined in 1985 and 1988 using a sequential extraction procedure were reassessed to explain the variations in the δ114Cd values determined in this study. The redox conditions in the mudflat soil were found to change from suboxic (Eh 300 mV) to anoxic (Eh –100 mV) at 20 cm. This was caused by semi-diurnal flooding with oxygenated river water (tidal pumping). The δ114Cd values varied systematically with depth and were correlated with the redox profile. The intense tidal water flow caused lighter Cd isotopes to desorb more readily from the parent soil in the upper suboxic zone and to subsequently redepositing in the deeper anoxic (sulfidic) zone, where the lighter Cd mobilized from Fe/Mn oxyhydroxides was found to be scavenged in sulfidic form. Tidal advection of dissolved lighter Cd down to the anoxic zone and sulfidic reprecipitation led to a decrease in δ114Cd value of up to -0.2‰ with signals of ±0.1‰ even on a seasonal timescale. It became clear that apportioning sources using Cd isotopes would be difficult given the sensitivity of the isotope record to such early-diagenetic isotope fractionation reactions

Numerische Methode zur Bestimmung der Fahrwerkskonfiguration aus Baukastenkomponenten

Numerische Methode zur Bestimmung der Fahrwerkskonfiguration aus Baukastenkomponente

On the stability of periodic orbits in delay equations with large delay

We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is characterized by a set of curves, which we call asymptotic continuous spectrum, that is independent on the delay.Comment: postprint versio

High-frequency pulsations in DFB-lasers with amplified feedback

We describe the basic ideas behind the concept of DFB-lasers with short optical feedback for the generation of high-frequency self-pulsations (SPs) and show the theoretical background describing realized devices. It is predicted by theory that the SP frequency increases with increasing feedback strength. To provide evidence for this we propose a novel device design which employs an amplifier section in the integrated feedback cavity of a DFB-laser. We present results from numerical simulations and experiments. It has been shown experimentally that a continuous tuning of the SP frequency from 12 to 45GHz can be adjusted via the control of the feedback strength. The numerical simulations which are in good accordance with experimental investigations give an explanation for a self stabilizing effect of the SPs due to the additional carrier dynamic in the integrated feedback cavity