Network


Latest external collaboration on country level. Dive into details by clicking on the dots.

Hotspot


Dive into the research topics where Judith Lehnert is active.

Publication


Featured researches published by Judith Lehnert.


Physical Review E | 2012

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

Anton Selivanov; Judith Lehnert; Thomas Dahms; Philipp Hövel; Alexander L. Fradkov; Eckehard Schöll

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.


EPL | 2011

Loss of synchronization in complex neuronal networks with delay

Judith Lehnert; Thomas Dahms; Philipp Hövel; Eckehard Schöll

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.


Physical Review E | 2014

Controlling cluster synchronization by adapting the topology.

Judith Lehnert; Philipp Hövel; Anton Selivanov; Alexander L. Fradkov; Eckehard Schöll

We suggest an adaptive control scheme for the control of in-phase and cluster synchronization in delay-coupled networks. Based on the speed-gradient method, our scheme adapts the topology of a network such that the target state is realized. It is robust towards different initial conditions as well as changes in the coupling parameters. The emerging topology is characterized by a delicate interplay of excitatory and inhibitory links leading to the stabilization of the desired cluster state. As a crucial parameter determining this interplay we identify the delay time. Furthermore, we show how to construct networks such that they exhibit not only a given cluster state but also with a given oscillation frequency. We apply our method to coupled Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in an expansion of systems close to a Hopf bifurcation. The successful and robust control of this generic model opens up possible applications in a wide range of systems in physics, chemistry, technology, and life science.


Chaos | 2011

Adaptive Tuning of Feedback Gain in Time-Delayed Feedback Control

Judith Lehnert; Philipp Hövel; Valentin Flunkert; P. Yu. Guzenko; Alexander L. Fradkov; Eckehard Schöll

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.


European Physical Journal B | 2014

Heterogeneous delays in neural networks

Caglar Cakan; Judith Lehnert; Eckehard Schöll

Abstract We investigate heterogeneous coupling delays in complex networks of excitable elements described by the FitzHugh-Nagumo model. The effects of discrete as well as of uni- and bimodal continuous distributions are studied with a focus on different topologies, i.e., regular, small-world, and random networks. In the case of two discrete delay times resonance effects play a major role: depending on the ratio of the delay times, various characteristic spiking scenarios, such as coherent or asynchronous spiking, arise. For continuous delay distributions different dynamical patterns emerge depending on the width of the distribution. For small distribution widths, we find highly synchronized spiking, while for intermediate widths only spiking with low degree of synchrony persists, which is associated with traveling disruptions, partial amplitude death, or subnetwork synchronization, depending sensitively on the network topology. If the inhomogeneity of the coupling delays becomes too large, global amplitude death is induced.


European Physical Journal B | 2012

Synchronisation in networks of delay-coupled type-I excitable systems

Andrew Keane; Thomas Dahms; Judith Lehnert; Sachin Aralasurali Suryanarayana; Philipp Hövel; Eckehard Schöll

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.


Physical Review E | 2014

Synchronization-desynchronization transitions in complex networks: an interplay of distributed time delay and inhibitory nodes.

Carolin Wille; Judith Lehnert; Eckehard Schöll

We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart-Landau oscillators. To this end a symmetric network model is proposed for which the stability can be investigated analytically. It is found that beyond a critical inhibition ratio, synchronization tends to be unstable. However, increasing distributional widths can counteract this trend, leading to multiple resynchronization transitions at relatively high inhibition ratios. The extended applicability of the results is confirmed by numerical studies on asymmetrically perturbed network topologies. All investigations are performed on two distribution types, a uniform distribution and a Γ distribution.


Physical Review E | 2013

Adaptation controls synchrony and cluster states of coupled threshold-model neurons.

Josef Ladenbauer; Judith Lehnert; Hadi Rankoohi; Thomas Dahms; Eckehard Schöll; Klaus Obermayer

We analyze zero-lag and cluster synchrony of delay-coupled nonsmooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory and inhibitory neurons we find (i) that subthreshold adaptation stabilizes or destabilizes synchrony depending on whether the recurrent synaptic excitatory or inhibitory couplings dominate, and (ii) that synchrony is always unstable for networks with balanced recurrent synaptic inputs. If couplings are not too strong, synchronization properties are similar for very different coupling topologies, i.e., random connections or spatial networks with localized connectivity. We generalize our approach for two subpopulations of neurons with nonidentical local dynamics, including bursting, for which activity-based adaptation controls the stability of cluster states, independent of a specific coupling topology.


International Journal of Modern Physics B | 2012

CONTROL OF SYNCHRONIZATION IN DELAY-COUPLED NETWORKS

Eckehard Schöll; Anton Selivanov; Judith Lehnert; Thomas Dahms; Philipp Hövel; Alexander L. Fradkov

We consider synchronization in networks of delay-coupled 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, e.g., in-phase oscillation, splay or various cluster states. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase, coupling strength, and delay time such that a desired state can be selected from an otherwise multistable regime.


EPL | 2017

Stability of amplitude chimeras in oscillator networks

Liudmila Tumash; Anna Zakharova; Judith Lehnert; Wolfram Just; Eckehard Schöll

We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size

Collaboration


Dive into the Judith Lehnert's collaboration.

Top Co-Authors

Avatar

Eckehard Schöll

Technical University of Berlin

View shared research outputs
Top Co-Authors

Avatar

Philipp Hövel

Humboldt University of Berlin

View shared research outputs
Top Co-Authors

Avatar

Thomas Dahms

Technical University of Berlin

View shared research outputs
Top Co-Authors

Avatar

Alexander L. Fradkov

Saint Petersburg State University

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Andrew Keane

Technical University of Berlin

View shared research outputs
Top Co-Authors

Avatar

Anna Zakharova

Technical University of Berlin

View shared research outputs
Top Co-Authors

Avatar

Josef Ladenbauer

Technical University of Berlin

View shared research outputs
Top Co-Authors

Avatar

Klaus Obermayer

Technical University of Berlin

View shared research outputs
Top Co-Authors

Avatar

Sergei A. Plotnikov

Saint Petersburg State University

View shared research outputs
Researchain Logo
Decentralizing Knowledge