FG Nichtlineare Dynamik und Kontrolle

30 Items

Recent Submissions
Influence of Sound on Empirical Brain Networks

Sawicki, Jakub ; Schöll, Eckehard (2021-04-22)

We analyze the influence of an external sound source in a network of FitzHugh–Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report synchronization patterns, induced by the frequency of the sound source. We show that the level of synchrony can be enhanced by choosing the frequency of the sound source and its amplitude as control parameters for s...

Solitary states in adaptive nonlocal oscillator networks

Berner, Rico ; Polanska, Alicja ; Schöll, Eckehard ; Yanchuk, Serhiy (2020-09-28)

In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the phase-locked solutions, the rotating waves, we provide a rigorous stability analysis. This analysis shows a strong dependence of their stability on the coupling ...

Desynchronization Transitions in Adaptive Networks

Berner, Rico ; Vock, Simon ; Schöll, Eckehard ; Yanchuk, Serhiy (2021-01-15)

Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In this Letter, we develop the master stability approach for a large class of adaptive networks. This approach allows for reducing the synchronization problem fo...

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

Gerster, Moritz ; Berner, Rico ; Sawicki, Jakub ; Zakharova, Anna ; Škoch, Antonín ; Hlinka, Jaroslav ; Lehnertz, Klaus ; Schöll, Eckehard (2020-12-14)

We study patterns of partial synchronization in a network of FitzHugh–Nagumo oscillators with empirical structural connectivity measured in human subjects. We report the spontaneous occurrence of synchronization phenomena that closely resemble the ones seen during epileptic seizures in humans. In order to obtain deeper insights into the interplay between dynamics and network topology, we perfor...

Remote pacemaker control of chimera states in multilayer networks of neurons

Ruzzene, Giulia ; Omelchenko, Iryna ; Sawicki, Jakub ; Zakharova, Anna ; Schöll, Eckehard ; Andrzejak, Ralph G. (2020-11-24)

Networks of coupled nonlinear oscillators allow for the formation of nontrivial partially synchronized spatiotemporal patterns, such as chimera states, in which there are coexisting coherent (synchronized) and incoherent (desynchronized) domains. These complementary domains form spontaneously, and it is impossible to predict where the synchronized group will be positioned within the network. Th...

Structural anomalies in brain networks induce dynamical pacemaker effects

Koulierakis, Ioannis ; Verganelakis, Dimitris A. ; Omelchenko, Iryna ; Zakharova, Anna ; Schöll, Eckehard ; Provata, Astero (2020-11-19)

Dynamical effects on healthy brains and brains affected by tumor are investigated via numerical simulations. The brains are modeled as multilayer networks consisting of neuronal oscillators whose connectivities are extracted from Magnetic Resonance Imaging (MRI) data. The numerical results demonstrate that the healthy brain presents chimera-like states where regions with high white matter conce...

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

Berner, Rico ; Sawicki, Jakub ; Schöll, Eckehard (2020-02-24)

We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuroscience and social sciences, as well as biology, engineering, and other disciplines. We show by theoretical analysis and computer simulations that multiplexing in a multilayer network with symmetry can induce various stable phase cluster stat...

Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps

Rybalova, E. ; Strelkova, G. ; Schöll, Eckehard ; Anishchenko, V. (2020-06-09)

We study relay and complete synchronization in a heterogeneous triplex network of discrete-time chaotic oscillators. A relay layer and two outer layers, which are not directly coupled but interact via the relay layer, represent rings of nonlocally coupled two-dimensional maps. We consider for the first time the case when the spatiotemporal dynamics of the relay layer is completely different fro...

Patterns of synchrony in complex networks of adaptively coupled oscillators

Berner, Rico (2020)

Kollektive Phänomene in Systemen von miteinander verbundenen dynamischen Einheiten sind allgegenwärtig in der Natur. Das Schwarmverhalten in Gruppen von Vögeln oder Fischen, das synchrone Blinken von Glühwürmchen oder auch das kohärente "Feuern" von Neuronen im menschlichen Gehirn sind nur einige Beispiele für kollektives Verhalten. Die Erforschung der Mechanismen, die zur Synchronisation führe...

Effect of topology upon relay synchronization in triplex neuronal networks

Drauschke, Fenja ; Sawicki, Jakub ; Berner, Rico ; Omelchenko, Iryna ; Schöll, Eckehard (2020-05-07)

Relay synchronization in complex networks is characterized by the synchronization of remote parts of the network due to their interaction via a relay. In multilayer networks, distant layers that are not connected directly can synchronize due to signal propagation via relay layers. In this work, we investigate relay synchronization of partial synchronization patterns like chimera states in three...

Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics

Andrzejak, Ralph G. ; Ruzzene, Giulia ; Schöll, Eckehard ; Omelchenko, Iryna (2020-03-17)

We numerically study a network of two identical populations of identical real-valued quadratic maps. Upon variation of the coupling strengths within and across populations, the network exhibits a rich variety of distinct dynamics. The maps in individual populations can be synchronized or desynchronized. Their temporal evolution can be periodic or aperiodic. Furthermore, one can find blends of s...

Stability and control of power grids with diluted network topology

Tumash, Liudmila ; Olmi, Simona ; Schöll, Eckehard (2019-12-09)

We consider sparse random networks of Kuramoto phase oscillators with inertia in order to mimic and investigate the dynamics emerging in high-voltage power grids. The corresponding natural frequencies are assumed to be bimodally Gaussian distributed, thus modeling the distribution of both power generators and consumers, which must be in balance. Our main focus is on the theoretical analysis of ...

Hierarchical frequency clusters in adaptive networks of phase oscillators

Berner, Rico ; Fialkowski, Jan ; Kasatkin, Dmitry ; Nekorkin, Vladimir ; Yanchuk, Serhiy ; Schöll, Eckehard (2019-10-23)

Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this paper, we investigate the dynamics of this system. We extend recent results on the appearance of hierarchical frequency multiclusters by investigating the e...

Synchronization of spiral wave patterns in two-layer 2D lattices of nonlocally coupled discrete oscillators

Bukh, Andrei V. ; Schöll, Eckehard ; Anischenko, Vadim Semenovich (2019-05-07)

The paper describes the effects of mutual and external synchronization of spiral wave structures in two coupled two-dimensional lattices of coupled discrete-time oscillators. Each lattice is given by a 2D N×N network of nonlocally coupled Nekorkin maps which model neuronal activity. We show numerically that spiral wave structures, including spiral wave chimeras, can be synchronized and establis...

Two-dimensional spatiotemporal complexity in dual-delayed nonlinear feedback systems: Chimeras and dissipative solitons

Brunner, Daniel ; Penkovsky, Bogdan ; Levchenko, Roman ; Schöll, Eckehard ; Larger, Laurent ; Maistrenko, Yuri (2018-10-09)

We demonstrate for a photonic nonlinear system that two highly asymmetric feedback delays can induce a variety of emergent patterns which are highly robust during the system’s global evolution. Explicitly, two-dimensional chimeras and dissipative solitons become visible upon a space-time transformation. Switching between chimeras and dissipative solitons requires only adjusting two system param...

Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form

Mehrmann, Volker ; Morandin, Riccardo ; Olmi, Simona ; Schöll, Eckehard (2018-10-18)

In view of highly decentralized and diversified power generation concepts, in particular with renewable energies, the analysis and control of the stability and the synchronization of power networks is an important topic that requires different levels of modeling detail for different tasks. A frequently used qualitative approach relies on simplified nonlinear network models like the Kuramoto mod...

Networks of coupled oscillators: From phase to amplitude chimeras

Banerjee, Tanmoy ; Biswas, Debabrata ; Ghosh, Debarati ; Schöll, Eckehard ; Zakharova, Anna (2018-11-30)

We show that amplitude-mediated phase chimeras and amplitude chimeras can occur in the same network of nonlocally coupled identical oscillators. These are two different partial synchronization patterns, where spatially coherent domains coexist with incoherent domains and coherence/incoherence referring to both amplitude and phase or only the amplitude of the oscillators, respectively. By changi...

Time-delayed feedback control of coherence resonance chimeras

Zakharova, Anna ; Semenova, Nadezhda ; Anishchenko, Vadim ; Schöll, Eckehard (2017-10-26)

Using the model of a FitzHugh-Nagumo system in the excitable regime, we investigate the influence of time-delayed feedback on noise-induced chimera states in a network with nonlocal coupling, i.e., coherence resonance chimeras. It is shown that time-delayed feedback allows for the control of the range of parameter values where these chimera states occur. Moreover, for the feedback delay close t...

Chimera states and the interplay between initial conditions and non-local coupling

Kalle, Peter ; Sawicki, Jakub ; Zakharova, Anna ; Schöll, Eckehard (2017-03-15)

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We study chimera states in a network of non-locally coupled Stuart-Landau oscillators. We investigate the impact of initial conditions in combination with non-local coupling. Based on an analytical argument, we show how the coupling phase and the coupling strength are link...

Nonlinearity of local dynamics promotes multi-chimeras

Omelchenko, Iryna ; Zakharova, Anna ; Hövel, Philipp ; Siebert, Julien ; Schöll, Eckehard (2015-08-06)

Chimera states are complex spatio-temporal patterns in which domains of synchronous and asynchronous dynamics coexist in coupled systems of oscillators. We examine how the character of the individual elements influences chimera states by studying networks of nonlocally coupled Van der Pol oscillators. Varying the bifurcation parameter of the Van der Pol system, we can interpolate between regula...