arXiv subjects

Eckehard Schöll

Publications and source records attributed to Eckehard Schöll.

At least 109 records · Page 6Linked to original sources

arXiv2012

Equation of motion method for Full Counting Statistics: Steady state superradiance

For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of cumulant generating function and system operators at lowest order, allows us to recover master equation results of the Full Counting Statistics for certain parameter regimes at very low cost of computation. The thermodynamic limit, that is not accessible with the master equation approach, can be derived analytically for different approximations.

quant-ph↗

arXiv2012

Cluster and group synchronization in delay-coupled networks

We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability approach, we find that the master stability function shows a discrete rotational symmetry depending on the number of groups. The coupling matrices that permit solutions on group or cluster synchronization manifolds show a very similar symmetry in their eigenvalue spectrum, which helps to simplify the evaluation of the master stability function. Our theory allows for the characterization of stability of different patterns of synchronized dynamics in networks with multiple delay times, multiple coupling functions, but also with multiple kinds of local dynamics in the networks' nodes. We illustrate our results by calculating stability in the example of delay-coupled semiconductor lasers and in a model for neuronal spiking dynamics.

nlin.CD↗

arXiv2012

Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.

nlin.AO↗

arXiv2012

Chaos synchronization in networks of delay-coupled lasers: Role of the coupling phases

We derive rigorous conditions for the synchronization of all-optically coupled lasers. In particular, we elucidate the role of the optical coupling phases for synchronizability by systematically discussing all possible network motifs containing two lasers with delayed coupling and feedback. Hereby we explain previous experimental findings. Further, we study larger networks and elaborate optimal conditions for chaos synchronization. We show that the relative phases between lasers can be used to optimize the effective coupling matrix.

nlin.CD↗

arXiv2012

Transition from spatial coherence to incoherence in coupled chaotic systems

We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we find characteristic spatial patterns such as wave-like profiles and study the transition from coherence to incoherence leading to spatial chaos. We analyze the origin of this transition based on numerical simulations and support the results by theoretical derivations identifying a critical coupling strength and a scaling relation of the coherent profiles. To demonstrate the universality of our findings we consider time-discrete as well as time-continuous chaotic models realized as logistic map and Rössler or Lorenz system, respectively. Thereby we establish the coherence-incoherence transition in networks of coupled identical oscillators.

nlin.CD↗

arXiv2011

Loss of synchronization in complex neuronal networks with delay

We investigate the stability of synchronization in networks of delay-coupled excitable neural oscillators. On the basis of the master stability function formalism, we demonstrate that synchronization is always stable for excitatory coupling independently of the delay and coupling strength. Superimposing inhibitory links randomly on top of a regular ring of excitatory coupling, which yields a small-world-like network topology, we find a phase transition to desynchronization as the probability of inhibitory links exceeds a critical value. We explore the scaling of the critical value in dependence on network properties. Compared to random networks, we find that small-world topologies are more susceptible to desynchronization via inhibition.

cond-mat.dis-nn↗

arXiv2011

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.

nlin.AO↗

arXiv2011

Strong and weak chaos in nonlinear networks with time-delayed couplings

We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for large delay times, and relate this to the condition for stable or unstable chaotic synchronization, respectively. In simulations of laser models and experiments with electronic circuits, we identify transitions from weak to strong and back to weak chaos upon monotonically increasing the coupling strength.

nlin.CD↗

arXiv2011

Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators

We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay or various cluster states, can be selected.

nlin.AO↗

arXiv2011

Loss of coherence in dynamical networks: spatial chaos and chimera states

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous Rössler systems reveal that intermediate, partially coherent states represent characteristic spatio-temporal patterns at the transition from coherence to incoherence.

nlin.AO↗

arXiv2010

Symmetry-breaking transitions in networks of nonlinear circuit elements

We investigate a nonlinear circuit consisting of N tunnel diodes in series, which shows close similarities to a semiconductor superlattice or to a neural network. Each tunnel diode is modeled by a three-variable FitzHugh-Nagumo-like system. The tunnel diodes are coupled globally through a load resistor. We find complex bifurcation scenarios with symmetry-breaking transitions that generate multiple fixed points off the synchronization manifold. We show that multiply degenerate zero-eigenvalue bifurcations occur, which lead to multistable current branches, and that these bifurcations are also degenerate with a Hopf bifurcation. These predicted scenarios of multiple branches and degenerate bifurcations are also found experimentally.

nlin.CD↗

arXiv2009

Time-delayed feedback control of delay-coupled neurosystems and lasers

We discuss applications of time-delayed feedback control to delay-coupled neural systems and lasers, in the framework of the FitzHugh-Nagumo neuron model and the Lang-Kobayashi laser model, respectively. In the context of neural systems, we will point out some complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns, or amplitude death, induced by delayed coupling in combination with delayed self-feedback in simple network motifs. For optical systems, we will show that multiple time-delayed feedback, realized by a Fabry-Perot resonator coupled to the laser, provides a valuable tool for the suppression of unwanted intensity pulsations, and leads to stable continuous-wave operation.

nlin.CD↗

arXiv2009

Broadband chaos generated by an opto-electronic oscillator

We study an opto-electronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly-stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive an approximate map that does an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultra-wide-band sensor networks.

nlin.CD↗

arXiv2009

Transient behavior in systems with time-delayed feedback

We investigate the transient times for the onset of control of steady states by time-delayed feedback. The optimization of control by minimising the transient time before control becomes effective is discussed analytically and numerically, and the competing influences of local and global features are elaborated. We derive an algebraic scaling of the transient time and confirm our findings by numerical simulations in dependence on feedback gain and time delay.

nlin.AO↗

arXiv2009

Feedback-dependent control of stochastic synchronization in coupled neural systems

We investigate the synchronization dynamics of two coupled noise-driven FitzHugh-Nagumo systems, representing two neural populations. For certain choices of the noise intensities and coupling strength, we find cooperative stochastic dynamics such as frequency synchronization and phase synchronization, where the degree of synchronization can be quantified by the ratio of the interspike interval of the two excitable neural populations and the phase synchronization index, respectively. The stochastic synchronization can be either enhanced or suppressed by local time-delayed feedback control, depending upon the delay time and the coupling strength. The control depends crucially upon the coupling scheme of the control force, i.e., whether the control force is generated from the activator or inhibitor signal, and applied to either component. For inhibitor self-coupling, synchronization is most strongly enhanced, whereas for activator self-coupling there exist distinct values of the delay time where the synchronization is strongly suppressed even in the strong synchronization regime. For cross-coupling strongly modulated behavior is found.

nlin.AO↗

arXiv2009

Regular spiking in asymmetrically delay-coupled FitzHugh-Nagumo systems

We study two delay-coupled FitzHugh-Nagumo systems, introducing a mismatch between the delay times, as the simplest representation of interacting neurons. We demonstrate that the presence of delays can cause periodic oscillations which coexist with a stable fixed point. Periodic solutions observed are of two types, which we refer to as a "long" and a "short" cycle, respectively.

nlin.AO↗

arXiv2009

Dynamics of electronic transport in a semiconductor superlattice with a shunting side layer

We study a model describing electronic transport in a weakly-coupled semiconductor superlattice with a shunting side layer. Key parameters include the lateral size of the superlattice, the connectivity between the quantum wells of the superlattice and the shunt layer, and the conduction properties of the shunt layer. For a superlattice with small lateral extent and high quality shunt, static electric field domains are suppressed and a spatially-uniform field configuration is predicted to be stable, a result that may be useful for proposed devices such as a superlattice-based TeraHertz (THz) oscillators. As the lateral size of the superlattice increases, the uniform field configuration loses its stability to either static or dynamic field domains, regardless of shunt properties. A lower quality shunt generally leads to regular and chaotic current oscillations and complex spatio-temporal dynamics in the field profile. Bifurcations separating static and dynamic behaviors are characterized and found to be dependent on the shunt properties.

cond-mat.mtrl-sci↗

arXiv2008

Stabilizing continuous-wave output in semiconductor lasers by time-delayed feedback

The stabilization of steady states is studied in a modified Lang-Kobayashi model of a semiconductor laser. We show that multiple time-delayed feedback, realized by a Fabry-Perot resonator coupled to the laser, provides a valuable tool for the suppression of unwanted intensity pulsations, and leads to stable continuous-wave operation. The domains of control are calulated in dependence on the feedback strength, delay time (cavity round trip time), memory parameter (mirror reflectivity), latency time, feedback phase, and bandpass filtering, Due to the optical feedback, multistable behavior can also occur in the form of delay-induced intensity pulsations or other modes for certain choices of the control parameters. Control may then still be achieved by slowly ramping the injection current during turn-on.

nlin.CD↗