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

- [1]
- © Chaos, Volume 30, Issue 12

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)
[2]

AIP Science Highlight (Scilight) [3]

## Organizing bacterial vortex lattices by periodic obstacle arrays

- [4]
- © HR, DN, SH, AS, MB, SK, IA

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)
[5]

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

- [6]
- © LR, JS, AZ, JH, JC, ES

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) [7]

Article [8] on Phys.org

## Heat flow due to time-delayed feedback

- [9]
- © SL, SK

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)
[10]

## Wigner Time Delay Induced by a Single Quantum Dot

- [11]
- © MS, AC, JS, MH, CS, SH, JW, SR

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) [12]

## 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) [13]

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

- [14]
- © HR, SH, SK, MB

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) [15]

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

Aras Bacho, Etienne Emmrich,
Alexander Mielke

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

[16]

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

- [17]
- © FA, MWHR, KO

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) [18]

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

- [19]
- © RB, CS, HS

Reinier van Buel, Chistian Schaaf, Holger Stark

Reference: Euro. Phys. Lett. 124, 14001 (2018) [20]

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

- [21]
- © JT, JR, MT, KS, HE

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) [22]

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

- [23]
- © DP, AV, AP, SG, SY

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) [24]

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

- [25]
- © SB, MS, AC, PS, AT, MG, JS, AS, SR, AK, SR

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) [26]

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

- [27]
- © NS, AZ, VS, ES

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) [28]

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

- [29]
- © TW, PS, JB, ER, TB, RH

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) [30]

- [31]
- © TU Berlin

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.

flyer [32]

springer page [33]

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

- [34]
- © TU Berlin

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 [35]

## Tweezers for Chimeras in Small Networks

- [36]
- © IO, OO, AZ, MW, ES

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) [37]

## Pattern Formation in Systems with Multiple Delayed Feedbacks

- [38]
- © SY, GG

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) [39]

## Chimera Death: Symmetry Breaking in Dynamical Networks

- [40]
- © TU Berlin

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) [41]

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

- [42]
- © VB, PF, MV, TB

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) [43]

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

- [44]
- © JL, HE

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) [45]

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

- [46]
- © IO, OEO, PH, ES

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) [47]

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

- [48]
- © DPR, DR, DJG, ES

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) [49]

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

- [50]
- © SA, MB

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) [51]

## Thermodynamics of a physical model implementing a Maxwell demon

- [52]
- © TU Berlin

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) [53]

Highlighted
in Phys.org (2013) [54]

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

- [55]
- © AC, JK, FS, SR, AK

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) [56]

## Synchronized tumbling particles

- [57]
- © SK

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) [58]

## Experimental Observation of Chimeras in Coupled-Map Lattices

- [59]
- © AH, TM, RR, PH, IO, ES

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) [60]

Highlighted in
Physics Today (2012) [61]

Also highlighted in Physics Today, Search
and Discovery (2012) [62]

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

- [63]
- © TU Berlin

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) [64]

## 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

- [65]
- © MB, ES, AT

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.

Reference: Angewandte Chemie International Edition (2012) [66]

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

- [67]
- © TU Berlin

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 [68]

## Charge Qubit Purification by an Electronic Feedback Loop

- [69]
- © Copyright??

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) [70]

arXiv:1102.3771 [71]

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