TY  - JOUR
A1  - Voss, Henning U.
A1  - Kurths, Jürgen
T1  - Reconstruction of nonlinear time-delayed feedback models from optical data
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Ziehmann, Christine
A1  - Smith, L.
A1  - Kurths, Jürgen
T1  - The bootstrap and lyapunov exponents in deterministic chaos
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Kurths, Jürgen
T1  - Modeling Cognitive Control in Simple Movements
Y1  - 1999
SN  - 1-563-96863-0
ER  - 
TY  - JOUR
A1  - Kolodner, P.
A1  - Abel, Markus
A1  - Kurths, Jürgen
A1  - Voss, Henning U.
T1  - Amplitude equations from spatiotemporal binary-fluid convection data
Y1  - 1999
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/PRL83-3422.pdf
ER  - 
TY  - JOUR
A1  - Schwache, A.
A1  - Kurths, Jürgen
A1  - Mitschke, F.
A1  - Voss, Henning U.
T1  - Equations of motion from chaotic data : a driven optical fiber ring resonator
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Braun, Robert
A1  - Feudel, Fred
A1  - Gebogi, C.
A1  - Kurths, Jürgen
A1  - Witt, Annette
T1  - Tracer dynamics in a flow of driven vortices
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Abel, Hans-Henning
A1  - Kurths, Jürgen
A1  - Schäfer, Carsten
T1  - Synchronization in the human cardiorespiratory system
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Park, Eun Hyoung
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
A1  - Zaks, Michael A.
T1  - Alternating locking ratios in imperfect phase synchronization
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Heuer, Axel
A1  - Schultheiss, J.
A1  - Hodgson, N.
A1  - Kurths, Jürgen
A1  - Menzel, Ralf
A1  - Raab, Volker
T1  - Transverse effects in phase conjugate laser mirrors based on stimulated brillouin scattering
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Schwarz, Udo
A1  - Spahn, Frank
A1  - Grebogi, Celso
A1  - Kurths, Jürgen
A1  - Petzschmann, Olaf
T1  - Length scales of clustering in granular gases
Y1  - 1999
ER  - 
TY  - GEN
A1  - Motter, Adilson E.
A1  - Matias, Manuel A.
A1  - Kurths, Jürgen
A1  - Ott, Edward
T1  - Dynamics on complex networks and applications
T2  - Physica. D, Nonlinear phenomena
KW  - complex systems
KW  - nonlinear dynamics
KW  - statistical physics
Y1  - 2006
U6  - https://doi.org/10.1016/j.physd.2006.09.012
SN  - 0167-2789
VL  - 224
IS  - 1-2
SP  - VII
EP  - VIII
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Zemanova, Lucia
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Structural and functional clusters of complex brain networks
JF  - Physica, D, Nonlinear phenomena
N2  - Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.
KW  - cortical network
KW  - anatomical connectivity
KW  - functional connectivity
KW  - topological community
KW  - dynamical cluster
Y1  - 2006
U6  - https://doi.org/10.1016/j.physd.2006.09.008
SN  - 0167-2789
SN  - 1872-8022
VL  - 224
IS  - 1-2
SP  - 202
EP  - 212
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Meucci, Riccardo
A1  - Salvadori, Francesco
A1  - Ivanchenko, Mikhail V.
A1  - Al Naimee, Kais
A1  - Zhou, Chansong
A1  - Arecchi, Fortunato Tito
A1  - Boccaletti, Stefano
A1  - Kurths, Jürgen
T1  - Synchronization of spontaneous bursting in a CO2 laser
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.
Y1  - 2006
U6  - https://doi.org/10.1103/PhysRevE.74.066207
SN  - 2470-0045
SN  - 2470-0053
VL  - 74
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Synchronization approach to analysis of biological systems
N2  - In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach
Y1  - 2004
SN  - 0219-4775
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
T1  - Comment on "Phase synchronization in discrete chaotic systems"
N2  - Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Popovych, Orest
A1  - Maistrenko, Yu
A1  - Mosekilde, Erik
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Transcritical riddling in a system of coupled maps
N2  - The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
T1  - Phase synchronization in regular and chaotic systems
Y1  - 2000
SN  - 0218-1274
ER  - 
TY  - BOOK
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
T1  - Synchronization : a universal concept in nonlinear sciences
T3  - Cambridge nonlinear science series
Y1  - 2001
SN  - 0-521-59285-2
VL  - 12
PB  - Cambridge Univ. Press
CY  - Cambridge
ET  - 1st paperback ed., repr
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Zaks, Michael A.
A1  - Kurths, Jürgen
T1  - Phase synchronization of regular and chaotic oscillators
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Popovych, Orest
A1  - Maistrenko, Yu
A1  - Mosekilde, Erik
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Transcritical loss of synchronization in coupled chaotic systems
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - On the generalized dimensions for the fourier spectrum of the thue-morse sequence
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Tass, Peter
A1  - Rosenblum, Michael
A1  - Weule, J.
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
A1  - Volkmann, J.
A1  - Schnitzler, A.
A1  - Freund, H.-J.
T1  - Detection of n:m phase locking from noisy data : application to magnetoencephalography
N2  - We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - From Phase to Lag Synchronization in Coupled Chaotic Oscillators
N2  - We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe thisregime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Coherence Resonance in a Noise-Driven Excitable System
N2  - We study the dynamics of the excitable Fitz Hugh-Nagumo system under external noisy driving. Noise activates the system producing a sequence of pulses. The coherence of these noise-induced oscillations is shown to be maximal for a certain noise amplitude. This new effect of coherence resonance is explained by different noise dependencies of the activation and the excursion times. A simple one-dimensional model based on the Langevin dynamics is proposed for the quantitative description of this phenomenon.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
A1  - Schafer, C.
A1  - Tass, Peter
A1  - Abel, Hans-Henning
T1  - Synchronization in Noisy Systems and Cardiorespiratory Interaction
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Ruzick, Oliver
A1  - Scheffczyk, Christian
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Dynamics of chaos-order interface in coupled map lattices
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Symbolic dynamics behind the singular continuous power spectra of continuous flows
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Witt, Annette
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
T1  - Testing stationarity in time series
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization in noisy and chaotic oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - On the correlation dimension of the spectral measure for the Thue-Morse sequence
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization in driven and coupled chaotic oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Effect of phase synchronization in driven chaotic oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Coherence resonance in a noise-driven excitable system
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Romano, Maria Carmen
A1  - Thiel, M.
A1  - Kurths, Jürgen
A1  - Kiss, Istvan Z.
A1  - Hudson, J. L.
T1  - Detection of synchronization for non-phase-coherent and non-stationary data
N2  - We present a new method to detect phase as well as generalized synchronization in a wide class of complex systems. It is based on the recurrences of the system's trajectory to the neighborhood of a former state in phase space. We illustrate the applicability of the algorithm for the paradigmatic chaotic Rossler system in the funnel regime and for noisy data, where other methods to detect phase synchronization fail. Furthermore, we demonstrate for electrochemical experiments that the method can easily detect phase and generalized synchronization in non-phase- coherent and even non-stationary time series
Y1  - 2005
SN  - 0295-5075
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
A1  - Kiss, Istvan Z.
A1  - Hudson, J. L.
T1  - Noise-enhanced phase synchronization of chaotic oscillators
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Stolbova, Veronika
A1  - Surovyatkina, Elena
A1  - Bookhagen, Bodo
A1  - Kurths, Jürgen
T1  - Tipping elements of the Indian monsoon: Prediction of onset and
withdrawal
JF  - Geophysical research letters
N2  - Forecasting the onset and withdrawal of the Indian summer monsoon is crucial for the life and prosperity of more than one billion inhabitants of the Indian subcontinent. However, accurate prediction of monsoon timing remains a challenge, despite numerous efforts. Here we present a method for prediction of monsoon timing based on a critical transition precursor. We identify geographic regions-tipping elements of the monsoon-and use them as observation locations for predicting onset and withdrawal dates. Unlike most predictability methods, our approach does not rely on precipitation analysis but on air temperature and relative humidity, which are well represented both in models and observations. The proposed method allows to predict onset 2 weeks earlier and withdrawal dates 1.5 months earlier than existing methods. In addition, it enables to correctly forecast monsoon duration for some anomalous years, often associated with El Nino-Southern Oscillation.
Y1  - 2016
U6  - https://doi.org/10.1002/2016GL068392
SN  - 0094-8276
SN  - 1944-8007
VL  - 43
SP  - 3982
EP  - 3990
PB  - American Geophysical Union
CY  - Washington
ER  - 
TY  - JOUR
A1  - Boers, Niklas
A1  - Goswami, Bedartha
A1  - Rheinwalt, Aljoscha
A1  - Bookhagen, Bodo
A1  - Hoskins, Brian
A1  - Kurths, Jürgen
T1  - Complex networks reveal global pattern of extreme-rainfall teleconnections
JF  - Nature : the international weekly journal of science
N2  - Climatic observables are often correlated across long spatial distances, and extreme events, such as heatwaves or floods, are typically assumed to be related to such teleconnections(1,2). Revealing atmospheric teleconnection patterns and understanding their underlying mechanisms is of great importance for weather forecasting in general and extreme-event prediction in particular(3,4), especially considering that the characteristics of extreme events have been suggested to change under ongoing anthropogenic climate change(5-8). Here we reveal the global coupling pattern of extreme-rainfall events by applying complex-network methodology to high-resolution satellite data and introducing a technique that corrects for multiple-comparison bias in functional networks. We find that the distance distribution of significant connections (P < 0.005) around the globe decays according to a power law up to distances of about 2,500 kilometres. For longer distances, the probability of significant connections is much higher than expected from the scaling of the power law. We attribute the shorter, power-law-distributed connections to regional weather systems. The longer, super-power-law-distributed connections form a global rainfall teleconnection pattern that is probably controlled by upper-level Rossby waves. We show that extreme-rainfall events in the monsoon systems of south-central Asia, east Asia and Africa are significantly synchronized. Moreover, we uncover concise links between south-central Asia and the European and North American extratropics, as well as the Southern Hemisphere extratropics. Analysis of the atmospheric conditions that lead to these teleconnections confirms Rossby waves as the physical mechanism underlying these global teleconnection patterns and emphasizes their crucial role in dynamical tropical-extratropical couplings. Our results provide insights into the function of Rossby waves in creating stable, global-scale dependencies of extreme-rainfall events, and into the potential predictability of associated natural hazards.
Y1  - 2019
U6  - https://doi.org/10.1038/s41586-018-0872-x
SN  - 0028-0836
SN  - 1476-4687
VL  - 566
IS  - 7744
SP  - 373
EP  - 377
PB  - Nature Publ. Group
CY  - London
ER  - 
TY  - JOUR
A1  - Riedl, Maik
A1  - van Leeuwen, Peter Jan
A1  - Suhrbier, Alexander
A1  - Malberg, Hagen
A1  - Groenemeyer, Dietrich
A1  - Kurths, Jürgen
A1  - Wessel, Niels
T1  - Testing foetal-maternal heart rate synchronization via model-based analyses
N2  - The investigation of foetal reaction to internal and external conditions and stimuli is an important tool in the characterization of the developing neural integration of the foetus. An interesting example of this is the study of the interrelationship between the foetal and the maternal heart rate. Recent studies have shown a certain likelihood of occasional heart rate synchronization between mother and foetus. In the case of respiratory-induced heart rate changes, the comparison with maternal surrogates suggests that the evidence for detected synchronization is largely statistical and does not result from physiological interaction. Rather, they simply reflect a stochastic, temporary stability of two independent oscillators with time-variant frequencies. We reanalysed three datasets from that study for a more local consideration. Epochs of assumed synchronization associated with short-term regulation of the foetal heart rate were selected and compared with synchronization resulting from white noise instead of the foetal signal. Using data-driven modelling analysis, it was possible to identify the consistent influence of the heartbeat duration of maternal beats preceding the foetal beats during epochs of synchronization. These maternal beats occurred approximately one maternal respiratory cycle prior to the affected foetal beat. A similar effect could not be found in the epochs without synchronization. Simulations based on the fitted models led to a higher likelihood of synchronization in the data segments with assumed foetal-maternal interaction than in the segment without such assumed interaction. We conclude that the data-driven model-based analysis can be a useful tool for the identification of synchronization.
Y1  - 2009
UR  - http://rsta.royalsocietypublishing.org/
U6  - https://doi.org/10.1098/rsta.2008.0277
SN  - 1364-503X
ER  - 
TY  - JOUR
A1  - Ivanchenko, Mikhail V.
A1  - Osipov, Grigory V.
A1  - Shalfeev, V. D.
A1  - Kurths, Jürgen
T1  - Phase synchronization in ensembles of bursting oscillators
N2  - We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles
Y1  - 2004
SN  - 0031-9007
ER  - 
TY  - JOUR
A1  - Ivanchenko, Mikhail V.
A1  - Osipov, Grigory V.
A1  - Shalfeev, V. D.
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic intermittent oscillations
N2  - We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization
Y1  - 2004
SN  - 0031-9007
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase Synchronization of Chaotic Rotators
N2  - We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
A1  - Osipov, Grigory V.
A1  - Kiss, Istvan Z.
A1  - Hudson, J. L.
T1  - Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic oscillations in terms of periodic orbits
Y1  - 1997
SN  - 1054-1500
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Phase synchronization effects in a lattice of nonidentical Rössler oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic oscillators by external driving
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Boccaletti, Stefano
A1  - Kurths, Jürgen
A1  - Osipov, Grigory V.
T1  - The synchronization of chaotic systems
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Regular and chaotic phase synchronization of coupled circle maps
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Zaks, Michael A.
A1  - Kurths, Jürgen
T1  - Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization
N2  - The chaotically driven circle map is considered as the simplest model ofphase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-repeller collision. Beyond the transition an intermittent regime with exponentially rare phase slips, resulting from the trajectory's hits on an eyelet, is observed.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Ivanchenko, Mikhail V.
A1  - Osipov, Grigory V.
A1  - Shalfeev, V. D.
A1  - Kurths, Jürgen
T1  - Synchronization of two non-scalar-coupled limit-cycle oscillators
N2  - Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved
Y1  - 2004
ER  - 
TY  - JOUR
A1  - Belykh, Vladimir N.
A1  - Osipov, Grigory V.
A1  - Kuckländer, Nina
A1  - Blasius, Bernd
A1  - Kurths, Jürgen
T1  - Automatic control of phase synchronization in coupled complex oscillators
N2  - We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic R"ossler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic R"ossler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.
Y1  - 2005
UR  - http://www.agnld.uni-potsdam.de/~bernd/papers/physica_D.pdf
ER  -