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## FitzHugh–Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena

Moritz Gerster, Rico Berner, Jakub Sawicki, Anna Zakharova, Antonín Škoch, Jaroslav Hlinka, Klaus Lehnertz, and Eckehard Schöll

We study patterns of partial synchronization in a network of FitzHugh–Nagumo oscillators with empirical structural connectivity measuredin human subjects. We report the spontaneous occurrence of synchronization phenomena that closely resemble the ones seen during epilepticseizures in humans. In order to obtain deeper insights into the interplay between dynamics and network topology, we perform long-term sim-ulations of oscillatory dynamics on different paradigmatic network structures: random networks, regular nonlocally coupled ring networks,ring networks with fractal connectivities, and small-world networks with various rewiring probability. Among these networks, a small-worldnetwork with intermediate rewiring probability best mimics the findings achieved with the simulations using the empirical structural con-nectivity. For the other network topologies, either no spontaneously occurring epileptic-seizure-related synchronization phenomena can beobserved in the simulated dynamics, or the overall degree of synchronization remains high throughout the simulation. This indicates thata topology with some balance between regularity and randomness favors the self-initiation and self-termination of episodes of seizure-likestrong synchronization.

Reference: Chaos 30, 123130 (2020)

AIP Science Highlight (Scilight)

## Organizing bacterial vortex lattices by periodic obstacle arrays

Henning Reinken, Daiki Nishiguchi, Sebastian Heidenreich, Andrey Sokolov, Markus Bär, Sabine H. L. Klapp, Igor S. Aranson

Recent experiments have shown that the complex spatio-temporal vortex structures emerging in active fluids are susceptible to weak geometrical constraints. This observation poses the fundamental question of how boundary effects stabilize a highly ordered pattern from seemingly turbulent motion. Here we show, by a combination of continuum theory and experiments on a bacterial suspension, how artificial obstacles guide the flow profile and reorganize topological defects, which enables the design of bacterial vortex lattices with tunable properties. To this end, the continuum model is extended by appropriate boundary conditions. Beyond the stabilization of square and hexagonal lattices, we also provide a striking example of a chiral, antiferromagnetic lattice exhibiting a net rotational flow, which is induced by arranging the obstacles in a Kagome-like array.

Reference: Commun. Phys. 3, 76 (2020)

## Partial synchronization in empirical brain networks as a model for unihemispheric sleep

Lukas Ramlow, Jakub Sawicki, Anna Zakharova, Jaroslav Hlinka, Jens Christian Claussen and Eckehard Schöll

We analyze partial synchronization patterns in a network of FitzHugh-Nagumo os- cillators with empirical structural connectivity measured in healthy human subjects. We report a dynamical asymmetry between the hemispheres, induced by the natural structural asymmetry. We show that the dynamical asymmetry can be enhanced by introducing the inter-hemispheric cou- pling strength as a control parameter for partial synchronization patterns. We discuss a minimum model elucidating the modalities of unihemispheric sleep in human brain, where one hemisphere sleeps while the other remains awake. In fact, this state is common among migratory birds and mammals like aquatic species.

Reference: Eur. Phys. Lett. 126, 50007 (2019)

Article on Phys.org

## Heat flow due to time-delayed feedback

Sarah Loos, Sabine H. L. Klapp

Many stochastic systems in biology, physics and technology involve discrete time delays in the underlying equations of motion, stemming, e. g., from finite signal transmission times, or a time lag between signal detection and adaption of an apparatus. From a mathematical perspective, delayed systems represent a special class of non-Markovian processes with delta-peaked memory kernels. It is well established that delays can induce intriguing behaviour, such as spontaneous oscillations, or resonance phenomena resulting from the interplay between delay and noise. However, the thermodynamics of delayed stochastic systems is still widely unexplored. This is especially true for continuous systems governed by nonlinear forces, which are omnipresent in realistic situations. We here present an analytical approach for the net steady-state heat rate in classical overdamped systems subject to time-delayed feedback. We show that the feedback inevitably leads to a finite heat flow even for vanishingly small delay times, and detect the nontrivial interplay of noise and delay as the underlying reason. To illustrate this point, and to provide an understanding of the heat flow at small delay times below the velocity-relaxation timescale, we compare with the case of underdamped motion where the phenomenon of “entropy pumping” has already been established. Application to an exemplary (overdamped) bistable system reveals that the feedback induces heating as well as cooling regimes and leads to a maximum of the medium entropy production at coherence resonance conditions. These observations are, in principle, measurable in experiments involving colloidal suspensions.

Reference: Sci. Rep. 9, 2491 (2019)

## Wigner Time Delay Induced by a Single Quantum Dot

Max Strauß, Alexander Carmele, Julian Schleibner, Marcel Hohn, Christian Schneider, Sven Höfling, Janik Wolters, and Stephan Reitzenstein

Resonant scattering of weak coherent laser pulses on a single two-level system realized in a semiconductor quantum dot is investigated with respect to a time delay between incoming and scattered light. This type of time delay was predicted by Wigner in 1955 for purely coherent scattering and was confirmed for an atomic system in 2013 [R. Bourgain et al., Opt. Lett. 38, 1963 (2013)]. In the presence of electron-phonon interaction, we observe deviations from Wigner’s theory related to incoherent and strongly non-Markovian scattering processes which are hard to quantify via a detuning-independent pure dephasing time. We observe detuning-dependent Wigner delays of up to 530 ps in our experiments which are supported quantitatively by microscopic theory allowing for pure dephasing times of up to 950 ps.

Reference: Phys. Rev. Lett. 122, 107401 (2019)

## Robust port-Hamiltonian representations of passive systems

Christopher A. Beattie, Volker Mehrmann, Paul Van Dooren

We discuss robust representations of stable, passive systems in particular coordinate systems, focussing especially on *port-Hamiltonian* representations. Such representations are typically not unique and the degrees of freedom associated with nonuniqueness are related to the solution set of the Kalman–Yakubovich–Popov linear matrix inequality (LMI). In this paper we analyze robustness measures for different possible port-Hamiltonian representations and relate it to quality functions defined in terms of eigenvalues of the matrix solution of the LMI. In particular, we look at the analytic center of this LMI. Within this framework, we derive inequalities for the passivity radius of the given model representation.

Reference: Automatica 100, 182 (2019)

## Anisotropic mesoscale turbulence and pattern formation in microswimmer suspensions induced by orienting external fields

Henning Reinken, Sebastian Heidenreich, Markus Bär, Sabine H. L. Klapp

This paper studies the influence of orienting external fields on pattern formation, particularly mesoscale turbulence, in microswimmer suspensions. To this end, we apply a hydrodynamic theory that can be derived from a microscopic microswimmer model (Reinken *et al *2018 *Phys. Rev. *E **97**, 022613). The theory combines a dynamic equation for the polar order parameter with a modified Stokes equation for the solvent flow. Here, we extend the model by including an external field that exerts an aligning torque on the swimmers (mimicking the situation in chemo-, photo-, magneto- or gravitaxis). Compared to the field-free case, the external field breaks the rotational symmetry of the vortex dynamics and leads instead to strongly asymmetric, traveling stripe patterns, as demonstrated by numerical solution and linear stability analysis. We further analyze the emerging structures using a reduced model which involves only an (effective) microswimmer velocity field. This model is significantly easier to handle analytically, but still preserves the main features of the anisotropic pattern formation. We observe an underlying transition between a square vortex lattice and a traveling stripe pattern. These structures can be well described in the framework of weakly nonlinear analysis, provided the strength of nonlinear advection is sufficiently weak.

Reference: New J. Phys. 21, 013037 (2019)

## An existence result and evolutionary Gamma-convergence for perturbed gradient systems

Aras Bacho, Etienne Emmrich, Alexander Mielke

Reference: J. Evol. Equat. 19, 479 (2019)

## Differential polarization of cortical pyramidal neuron dendrites through weak extracellular fields

Florian Aspart, Michiel W. H. Remme, Klaus Obermayer

The rise of transcranial current stimulation (tCS) techniques have sparked an increasing interest in the effects of weak extracellular electric fields on neural activity. These fields modulate ongoing neural activity through polarization of the neuronal membrane. While the somatic polarization has been investigated experimentally, the frequency-dependent polarization of the dendritic trees in the presence of alternating (AC) fields has received little attention yet. Using a biophysically detailed model with experimentally constrained active conductances, we analyze the subthreshold response of cortical pyramidal cells to weak AC fields, as induced during tCS. We observe a strong frequency resonance around 10-20 Hz in the apical dendrites sensitivity to polarize in response to electric fields but not in the basal dendrites nor the soma. To disentangle the relative roles of the cell morphology and active and passive membrane properties in this resonance, we perform a thorough analysis using simplified models, e.g. a passive pyramidal neuron model, simple passive cables and reconstructed cell model with simplified ion channels. We attribute the origin of the resonance in the apical dendrites to (i) a locally increased sensitivity due to the morphology and to (ii) the high density of h-type channels. Our systematic study provides an improved understanding of the subthreshold response of cortical cells to weak electric fields and, importantly, allows for an improved design of tCS stimuli.

Reference: PLOS Comput. Biol. 14(5), e1006124 (2018)

## Elastic turbulence in two-dimensional Taylor-Couette flows

Reinier van Buel, Chistian Schaaf, Holger Stark

Reference: Euro. Phys. Lett. 124, 14001 (2018)

## Spiral wave chimera states in large populations of coupled chemical oscillators

Jan Frederik Totz, Julian Rode, Mark R. Tinsley, Kenneth Showalter & Harald Engel

Our studies suggest that the spiral wave chimeras, core expansion and core splitting observed in the BZ system are likely to be found in a range of other systems with the common properties of immediate firing following a perturbation and long-range interactions. For example, we have found similar spiral wave chimera behaviour, with core splitting and the transition to predominantly asynchronous behaviour, in populations of nonlocally coupled FitzHugh–Nagumo oscillators. The PRC for the FitzHugh–Nagumo system resembles the PRC of the BZ system and ZBKE model, with an immediate firing region. Pulse coupled oscillator models of neuronal systems can also have immediate firing dynamics, suggesting that certain neuronal networks might exhibit spiral wave chimera behaviour similar to that described here. Other possible systems where these behaviours might be found include biological tissues and arrays of physical oscillators.

Reference: Nature Physics 14, 282 (2017)

## Bound Pulse Trains in Arrays of Coupled Spatially Extended Dynamical Systems

Dmitry Puzyrev, Andrei G. Vladimirov, Alexander Pimenov, Svetlana V. Gurevich & Serhiy Yanchuk

We study the dynamics of an array of nearest-neighbor coupled spatially distributed systems each generating a periodic sequence of short pulses. We demonstrate that, unlike a solitary system generating a train of equidistant pulses, an array of such systems can produce a sequence of clusters of closely packed pulses, with the distance between individual pulses depending on the coupling phase. This regime associated with the formation of locally coupled pulse trains bounded due to a balance of attraction and repulsion between them is different from the pulse bound states reported earlier in different laser, plasma, chemical, and biological systems. We propose a simplified analytical description of the observed phenomenon, which is in good agreement with the results of direct numerical simulations of a model system describing an array of coupled mode-locked lasers.

Reference: Phys. Rev. Lett. 119, 163901 (2017)

## Path-Controlled Time Reordering of Paired Photons in a Dressed Three-Level Cascade

Samir Bounouar, Max Strauß, Alexander Carmele, Peter Schnauber, Alexander Thoma, Manuel Gschrey, Jan-Hindrik Schulze, André Strittmatter, Sven Rodt, Andreas Knorr & Stephan Reitzenstein

The two-photon dressing of a “three-level ladder” system, here the ground state, the exciton, and the biexciton of a semiconductor quantum dot, leads to new eigenstates and allows one to manipulate the time ordering of the paired photons without unitary postprocessing. We show that, after spectral postselection of the single dressed states, the time ordering of the cascaded photons can be removed or conserved. Our joint experimental and theoretical study demonstrates the high potential of a “ladder” system to be a versatile source of orthogonally polarized, bunched or antibunched pairs of photons.

Reference: Phys. Rev. Lett. 118, 233601 (2017)

## Coherence-Resonance Chimeras in a Network of Excitable Elements

Nadezhda Semenova, Anna Zakharova, Vadim Anishchenko & Eckehard Schöll

We demonstrate that chimera behavior can be observed in nonlocally coupled networks of excitable systems in the presence of noise. This phenomenon is distinct from classical chimeras, which occur in deterministic oscillatory systems, and it combines temporal features of coherence resonance, i.e., the constructive role of noise, and spatial properties of chimera states, i.e., the coexistence of spatially coherent and incoherent domains in a network of identical elements. Coherence-resonance chimeras are associated with alternating switching of the location of coherent and incoherent domains, which might be relevant in neuronal networks.

Reference: Phys. Rev. Lett. 117, 014102 (2016)

## Strong suppression of shot noise in a feedback-controlled single-electron transistor

Timo Wagner, Philipp Strasberg, Johannes C. Bayer, Eddy P. Rugeramigabo, Tobias Brandes & Rolf J. Haug

Feedback control of quantum mechanical systems is rapidly attracting attention not only due to fundamental questions about quantum measurements but also because of its novel applications in many fields in physics. Quantum control has been studied intensively in quantum optics but progress has recently been made in the control of solid-state qubits as well. In quantum transport only a few active band passive feedback experiments have been realized on the level of single electrons, although theoretical proposals exist. Here we demonstrate the suppression of shot noise in a single-electron transistor using an exclusively electronic closed-loop feedback to monitor and adjust the counting statistics. With increasing feedback response we observe a stronger suppression and faster freezing of charge current fluctuations. Our technique is analogous to the generation of squeezed light with in-loop photodetection as used in quantum optics. Sub-Poisson single-electron sources will pave the way for high-precision measurements in quantum transport similar to optical or optomechanical equivalents.

Reference: Nat. Nanotechnol. 12, 218 (2016)

The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.

## Dynamics, control and information in delay-coupled systems

The International Conference on Delayed Complex Systems held from 4 to 8 June 2012 at the Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) in Palma de Mallorca, Spain, and co-organized with the Collaborative Research Center SFB 910 Control of Self-Organizing Nonlinear Systems—Theoretical Methods and Concepts of Application, Berlin, provided a forum for such topics. We took that opportunity to assemble a list of world leading experts, which now enables us to present perspectives of the state of the art in this field. This Theme Issue covers both applications and experiments, as well as mathematical foundations. The individual contributions summarize recent research results, but also address the broader context. Thus, the presentation is kept accessible for a large audience. The 14 articles cover various aspects of delay dynamics, control and information, ranging from fundamental mathematical aspects via delayed networks and time-delayed feedback control, to applications in neural science, optoelectronics and genetic control in cells. The articles are grouped into four parts.

http://rsta.royalsocietypublishing.org/content/371/1999.toc

## Tweezers for Chimeras in Small Networks

Iryna Omelchenko, Oleh E. Omel'chenko, Anna Zakharova, Matthias Wolfrum, and Eckehard Schöll

We propose a control scheme which can stabilize and fix the position of chimera states in small networks. Chimeras consist of coexisting domains of spatially coherent and incoherent dynamics in systems of nonlocally coupled identical oscillators. Chimera states are generally difficult to observe in small networks due to their short lifetime and erratic drifting of the spatial position of the incoherent domain. The control scheme, like a tweezer, might be useful in experiments, where usually only small networks can be realized.

Reference: Phys. Rev. Lett. 116, 114101 (2016)

## Pattern Formation in Systems with Multiple Delayed Feedbacks

Serhiy Yanchuk and Giovanni Giacomelli

Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities.

In this Letter, we introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. The behavior in the case of two delays is shown to “encode” two-dimensional spiral defects and defects turbulence. A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation, and a novel criterium for the attainment of the longdelay regime is introduced. We also demonstrate this phenomenon for a semiconductor laser with two delayed optical feedbacks.

Reference: Phys. Rev. Lett. 112, 174103 (2014)

## Chimera Death: Symmetry Breaking in Dynamical Networks

Anna Zakharova, Marie Kapeller, and Eckehard Schöll

For a network of generic oscillators with nonlocal topology and symmetry breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call “chimera death”. We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling, two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations and a direct abrupt transition for larger coupling strength.

Reference: Phys. Rev. Lett. 112, 154101 (2014)

## Quantum Criticality and Dynamical Instability in the Kicked-Top Model

Victor Manuel Bastidas, Pedro Pérez-Fernández, Malte Vogl, and Tobias Brandes

We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which is analogous to a continuous excited state quantum phase transition in undriven systems. We propose a protocol to observe the cusp behavior of the magnetization close to the critical quasienergy.

Reference: Phys. Rev. Lett. 112, 140408 (2014)

## Controlling the Position of Traveling Waves in Reaction-Diffusion Systems

Jakob Löber and Harald Engel

We present a method to control the position as a function of time of one-dimensional traveling wave solutions to reaction-diffusion systems according to a prespecified protocol of motion. Given this protocol, the control function is found as the solution of a perturbatively derived integral equation. Two cases are considered. First, we derive an analytical expression for the space (x) and time (t) dependent control function f(x,t) that is valid for arbitrary protocols and many reaction-diffusion systems. These results are close to numerically computed optimal controls. Second, for stationary control of traveling waves in one-component systems, the integral equation reduces to a Fredholm integral equation of the first kind. In both cases, the control can be expressed in terms of the uncontrolled wave profile and its propagation velocity, rendering detailed knowledge of the reaction kinetics unnecessary.

Reference: Phys. Rev. Lett. 112, 148305 (2014)

## When Nonlocal Coupling between Oscillators Becomes Stronger: Patched Synchrony or Multichimera States

Iryna Omelchenko, Oleh E. Omel’chenko, Philipp Hövel, and Eckehard Schöll

Systems of nonlocally coupled oscillators can exhibit complex spatiotemporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics. We report on a novel form of these states, found in a widely used model of a limit-cycle oscillator if one goes beyond the limit of weak coupling typical for phase oscillators. Then patches of synchronized dynamics appear within the incoherent domain giving rise to a multi-chimera state. We find that, depending on the coupling strength and range, different multichimera states arise in a transition from classical chimera states. The additional spatial modulation is due to strong coupling interaction and thus cannot be observed in simple phase-oscillator models.

Reference: Phys. Rev. Lett. 110, 224101 (2013)

## Control of Synchronization Patterns in Neural-like Boolean Networks

David P. Rosin, Damien Rontani, Daniel J. Gauthier, and Eckehard Schöll

We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the refractory time is on the same order of magnitude as the mean link time delays or the heterogeneities of the link time delays, cluster synchronization patterns change, or are suppressed entirely, respectively. We also show that these transitions occur when we change the properties of only a small number of driver nodes identified by their larger in degree; hence, the synchronization patterns can be controlled locally by these nodes. Our findings have implications for synchronization in biological neural networks.

Reference: Phys. Rev. Lett. 110, 104102 (2013)

## Reentry Near the Percolation Threshold in a Heterogeneous Discrete Model for Cardiac Tissue

Sergio Alonso, and Markus Bär

Arrhythmias in cardiac tissue are related to irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. A localized region with a fraction of nonconducting links surrounded by homogeneous conducting tissue can become a source of reentry and ectopic beats. Extensive simulations in a discrete model of cardiac tissue show that a wave crossing a heterogeneous region of cardiac tissue can disintegrate into irregular patterns, provided the fraction of nonconducting links is close to the percolation threshold of the cell network. The dependence of the reentry probability on this fraction, the system size, and the degree of excitability can be inferred from the size distribution of nonconducting clusters near the percolation threshold.

Reference: Phys. Rev. Lett. 110, 158101 (2013)

## Thermodynamics of a physical model implementing a Maxwell demon

Philipp Strasberg, Gernot Schaller, Tobias Brandes, and Massimiliano Esposito

We present a physical implementation of a Maxwell demon which consists of a conventional single electron transistor (SET) capacitively coupled to another quantum dot detecting its state. Altogether, the system is described by stochastic thermodynamics. We identify the regime where the energetics of the SET is not affected by the detection, but where its coarse-grained entropy production is shown to contain a new contribution compared to the isolated SET. This additional contribution can be identified as the information flow generated by the “Maxwell demon” feedback in an idealized limit.

Reference: Phys. Rev. Lett. 110, 040601 (2013)

Highlighted in Phys.org (2013)

## Single Photon Delayed Feedback: A Way to Stabilize Intrinsic Quantum Cavity Electrodynamics

Alexander Carmele, Julia Kabuss, Franz Schulze, Stephan Reitzenstein, and Andreas Knorr

Extrinsic and intrinsic control of non-classical photon states is of great importance in quantum information science. We investigate theoretically a single-emitter cavity system which operates initially in the weak-coupling limit. By applying an intrinsic control scheme, in particular quantum optical time-delayed self-feedback in the single-photon limit, we observe how this system is driven into the strong-coupling regime. This peculiar transition manifests in Rabi oscillations, observable in the coupled cavity field dynamics. This quantum optical apporach to time-delayed self-feedback opens new ways to experimentially controll features of cavity quantum electrodynamics in the single-photon limit.

Reference: Phys. Rev. Lett. 110, 013601 (2013)

## Synchronized tumbling particles

Sabine H. L. Klapp

Magnetic particles have been made that undergo synchronized oscillations when suspended in liquid in a rotating magnetic field. This discovery links the fields of nonlinear dynamics and materials science.

Reference: Nature 491, 530-531 (2012)

## Experimental Observation of Chimeras in Coupled-Map Lattices

Aaron M. Hagerstrom, Thomas E. Murphy, Rajarshi Roy, Philipp Hövel, Iryna Omelchenko and Eckehard Schöll

Networks of nonlocally coupled phase oscillators can support chimera states in which identical oscillators evolve into distinct groups that exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Similar nonlocal coupling topologies implemented in networks of chaotic iterated maps also yield dynamical states displaying coexisting spatial domains of coherence and incoherence. In these discrete-time systems, the phase is not a continuous variable, so these states are generalized chimeras with respect to a broader notion of incoherence. Chimeras continue to be the subject of intense theoretical investigation, but have yet to be realized experimentally. Here we show that these chimeras can be realized in experiments using a liquid crystal spatial light modulator to achieve optical nonlinearity in a spatially extended iterated map system. We study the coherence-incoherence transition that gives rise to these chimera states through experiment, theory, and simulation.

Reference: Nature Physics 8, 658 (2012)

Highlighted in Physics Today (2012)

Also highlighted in Physics Today, Search and Discovery (2012)

## Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

Iryna Omelchenko, Yuri Maistrenko, Philipp Hövel, and Eckehard Schöll

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatiotemporal 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 Rossler systems reveal that intermediate, partially coherent states represent characteristic spatiotemporal patterns at the transition from coherence to incoherence.

Reference: Phys. Rev. Lett. 106, 234102 (2011)

## Pattern-generation in delay-coupled neuronal systems

Serhiy Yanchuk and Markus Kantner

We show that an arbitrary periodic 2-dimensional spiking-patterns can be generated in a 2-dimensional lattice of unidirectionally delay-coupled neurons with appropriately tuned time-delayed couplings. The video shows an example: by appropriately choosing coupling delays, voltages in the array of 14x13 Hodgkin-Huxley neurons approach a stable attractor in the form of "SFB910" logo.

## Synchronization and Complex Dynamics of Oscillators with Delayed Pulse Coupling

Markus Bär, Eckehard Schöll, Alessandro Torcini

A systematic experimental study of pulse-coupled chemical oscillators with delay has confirmed a surprisingly large number of theoretical and mathematical predictions (see the dynamics for a pair of pulse-coupled oscillators; AP=antiphase (AP) and IP=in-phase oscillations, C=complex bursting dynamics, and OS=oscillator suppression). These results have implications for neuroscience and other biological fields.

## Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons

Josef Ladenbauer, Moritz Augustin, LieJune Shiau, Klaus Obermayer

Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how. A prominent feature of many types of neurons is spike frequency adaptation, shown by a decrease in spike rate during prolonged stimulation. This behavior is typically mediated by slow transmembrane potassium currents that can be controlled by the brains neuromodulatory systems. We investigated how these adaptation currents affect the synchronization tendency of synaptically coupled model neurons by applying phase reduction based on phase response curves (PRC). Therefore, we extended the adjoint method for calculating PRCs to dynamical systems with discontinuities. Using the experimentally verified and computationally efficient adaptive exponential integrate-and-fire model as well as a biophysically detailed neuron model for validation, we analyzed synchrony and phase locking of pairs and larger networks. We found that increased adaptation currents promote synchronization of coupled excitatory neurons at lower spike frequencies, as long as the conduction delays between the neurons are negligible. Inhibitory neurons on the other hand synchronize in presence of conduction delays, with or without adaptation currents. We conclude that in local populations of excitatory neurons adaptation currents provide a mechanism to generate low frequency oscillations that could be controlled through neuromodulation, while faster rhythms seem to be caused by inhibition rather than excitation. The study provides a first step towards understanding potential mechanisms underlying the top-down control of cortical states.

Reference: PLoS Comput Biol 8(4): e1002478. doi:10.1371/journal.pcbi.1002478

## Charge Qubit Purification by an Electronic Feedback Loop

We propose the manipulation of an isolated qubit by a simple instantaneous closed-loop feedback scheme in which a time-dependent electronic detector current is directly back-coupled into qubit parameters. As specific detector model we employ a capacitively coupled single-electron transistor. We demonstrate the stabilization of pure delocalized qubit states above a critical detector-qubit coupling. This electronic purification is independent of the initial qubit state and is accomplished after few electron jumps through the detector. Our simple scheme can be used for the efficient and robust initialization of solid-state qubits in quantum computational algorithms at arbitrary temperatures.

Gerold Kiesslich, Gernot Schaller, Clive Emary, and Tobias Brandes

Physical Review Letters **107**, 050501 (2011)

arXiv:1102.3771