FG Nichtlineare Dynamik und Kontrolle

21 Items

Recent Submissions
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...

Controlling chimera states via minimal coupling modification

Ruzzene, Giulia ; Omelchenko, Iryna ; Schöll, Eckehard ; Zakharova, Anna ; Andrzejak, Ralph G. (2019-05-07)

We propose a method to control chimera states in a ring-shaped network of nonlocally coupled phase oscillators. This method acts exclusively on the network’s connectivity. Using the idea of a pacemaker oscillator, we investigate which is the minimal action needed to control chimeras. We implement the pacemaker choosing one oscillator and making its links unidirectional. Our results show that a ...

Chimera states in networks of Van der Pol oscillators with hierarchical connectivities

Ulonska, Stefan ; Omelchenko, Iryna ; Zakharova, Anna ; Schöll, Eckehard (2016-09-22)

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We analyse chimera states in ring networks of Van der Pol oscillators with hierarchical coupling topology. We investigate the stepwise transition from a nonlocal to a hierarchical topology and propose the network clustering coefficient as a measure to establish a link betw...

Complex partial synchronization patterns in networks of delay-coupled neurons

Nikitin, D. ; Omelchenko, Iryna ; Zakharova, Anna ; Avetyan, M. ; Fradkov, Alexander L. ; Schöll, Eckehard (2019-07-22)

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for th...

Excitation of solitons in hexagonal lattices and ways of controlling electron transport

Chetverikov, A. P. ; Ebeling, W. ; Schöll, Eckehard ; Velarde, M. G. (2017-12-23)

We construct metastable long-living hexagonal lattices with appropriately modified Morse interactions and show that highly-energetic solitons may be excited moving along crystallographic axes. Studying the propagation, their dynamic changes and the relaxation processes it appears that lump solitons create in the lattice running local compressions. Based on the tight-binding model we investigate...

Time-delayed feedback control of coherence resonance near subcritical Hopf bifurcation: Theory versus experiment

Semenov, Vladimir ; Feoktistov, Alexey ; Vadivasova, Tatyana ; Schöll, Eckehard ; Zakharova, Anna (2015-03-23)

Using the model of a generalized Van der Pol oscillator in the regime of subcritical Hopf bifurcation, we investigate the influence of time delay on noise-induced oscillations. It is shown that for appropriate choices of time delay, either suppression or enhancement of coherence resonance can be achieved. Analytical calculations are combined with numerical simulations and experiments on an elec...

Chimera states in brain networks: Empirical neural vs. modular fractal connectivity

Chouzouris, Teresa ; Omelchenko, Iryna ; Zakharova, Anna ; Hlinka, Jaroslav ; Jiruska, Premysl ; Schöll, Eckehard (2018-04-09)

Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both the brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivat...

Theory of Coulomb induced signatures in two dimensional spectroscopy of colloidal quantum dots

Ginter, Anke (2019)

In this thesis, the interplay between the Brownian motion of colloidal quantum dots (QDs) and the position-dependent Coulomb coupling is investigated. The Coulomb interaction plays an important role since it changes the optical and electrical properties of nanostructures such as colloidal QDs, even in the case of non-overlapping electron wave functions. Due to the Coulomb coupling, the individ...

Filtering Suppresses Amplitude Chimeras

Banerjee, Tanmoy ; Bandyopadhyay, Biswabibek ; Zakharova, Anna ; Schöll, Eckehard (2019-02-11)

Amplitude chimera (AC) is an interesting chimera pattern that has been discovered recently and is distinct from other chimera patterns, like phase chimeras and amplitude mediated phase chimeras. Unlike other chimeras, in the AC pattern all the oscillators have the same phase velocity, however, the oscillators in the incoherent domain show periodic oscillations with randomly shifted origin. In t...

Chimeras in Multiplex Networks: Interplay of Inter- and Intra-Layer Delays

Sawicki, Jakub ; Ghosh, Saptarshi ; Jalan, Sarika ; Zakharova, Anna (2019-04-24)

Time delay in complex networks with multiple interacting layers gives rise to special dynamics. We study the scenarios of time delay induced patterns in a three-layer network of FitzHugh-Nagumo oscillators. The topology of each layer is given by a nonlocally coupled ring. For appropriate values of the time delay in the couplings between the nodes, we find chimera states, i.e., hybrid spatio-tem...