TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Rosenblum, Michael
A1  - Scheffczyk, Christian
A1  - Engbert, Ralf
A1  - Krampe, Ralf-Thomas
A1  - Kurths, Jürgen
T1  - Modeling qualitative changes in bimanual movements
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Hnatkova, Katarina
A1  - Vessel, N.
A1  - Voss, Andreas
A1  - Kurths, Jürgen
A1  - Sander, A.
A1  - Schirdewan, Alexander
A1  - Camm, A. J.
A1  - Malik, Marek
T1  - Multiparametric analysis of heart rate variability used for risk stratification among survivors of acute myocardial infarction
Y1  - 1998
SN  - 0895-2795
ER  - 
TY  - JOUR
A1  - Kurths, Jürgen
A1  - Kliem, Bernhard
A1  - Schwarz, Udo
A1  - Krüger, Albrecht
A1  - Urpo, S.
T1  - Multiresolution analysis of solar mm-wave bursts
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Romano, Maria Carmen
A1  - Thiel, Marco
A1  - Kurths, Jürgen
A1  - von Bloh, Werner
T1  - Multivariate recurrence plots
N2  - We propose a new approach to calculate recurrence plots of multivariate time series, based on joint recurrences in phase space. This new method allows to estimate dynamical invariants of the whole system, like the joint Renyi entropy of second order. We use this entropy measure to quantitatively study in detail the phase synchronization of two bidirectionally coupled chaotic systems and identify different types of transitions to chaotic phase synchronization in dependence on the coupling strength and the frequency mismatch. By means of this analysis we find several new phenomena, such a chaos-period-chaos transition to phase synchronization for rather large coupling strengths. (C) 2004 Elsevier B.V. All rights reserved
Y1  - 2004
SN  - 0375-9601
ER  - 
TY  - JOUR
A1  - Motter, Adilson E.
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Network synchronization, diffusion, and the paradox of heterogeneity
N2  - Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength. Here we offer a solution to this apparent paradox. Our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states. We show that, for a given degree distribution, the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum. This enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size. Numerical verification of the main results is provided for representative classes of small-world and scale-free networks
Y1  - 2005
SN  - 1063-651X
ER  - 
TY  - JOUR
A1  - Kurths, Jürgen
A1  - Seehafer, Norbert
A1  - Spahn, Frank
T1  - Nichtlineare Dynamik in der Physik : Forschungsbeispiele und Forschungstrends
Y1  - 1999
UR  - http://www.phil.uni-augsburg.de/dgksnd
SN  - 3-540-65329- 5
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - García-Ojalvo, Jordi
A1  - Schimansky-Geier, Lutz
A1  - Kurths, Jürgen
T1  - Noise induced propagation in monostable media
N2  - We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium i observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.
Y1  - 2002
UR  - http://link.aps.org/abstract/PRL/v88/e010601
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  - Baltanás, J. P.
A1  - Zaikin, Alexei A.
A1  - Feudel, Fred
A1  - Kurths, Jürgen
A1  - Sanjuan, Miguel Angel Fernández
T1  - Noise-induced effects in tracer dynamics
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Noise-induced phase synchronization and synchronization transitions in chaotic oscillators
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Noise-sustained and controlled synchronization of stirred excitable media by external forcing
N2  - Most of the previous studies on constructive effects of noise in spatially extended systems have focused on static media, e.g., of the reaction diffusion type. Because many active chemical or biological processes occur in a fluid environment with mixing, we investigate here the interplay among noise, excitability, mixing and external forcing in excitable media advected by a chaotic flow, in a two-dimensional FitzHugh-Nagumo model described by a set of reaction- advection-diffusion equations. In the absence of external forcing, noise may generate sustained coherent oscillations of the media in a range of noise intensities and stirring rates. We find that these noise-sustained oscillations can be synchronized by external periodic signals much smaller than the threshold. Analysis of the locking regions in the parameter space of the signal period, stirring rate and noise intensity reveals that the mechanism underlying the synchronization behaviour is a matching between the time scales of the forcing signal and the noise-sustained oscillations. The results demonstrate that, in the presence of a suitable level of noise, the stirred excitable media act as self-sustained oscillatory systems and become much easier to be entrained by weak external forcing. Our results may be verified in experiments and are useful to understand the synchronization of population dynamics of oceanic ecological systems by annual cycles
Y1  - 2005
SN  - 1367-2630
ER  - 
TY  - JOUR
A1  - Baptista, Murilo da Silva
A1  - Pereira, Tiago
A1  - Sartorelli, J. C.
A1  - Caldas, Ibere Luiz
A1  - Kurths, Jürgen
T1  - Non-transitive maps in phase synchronization
N2  - Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved
Y1  - 2005
ER  - 
TY  - JOUR
A1  - Marwan, Norbert
A1  - Kurths, Jürgen
T1  - Nonlinear analysis of bivariate data with cross recurrence plots
N2  - We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Nino data.
Y1  - 2001
UR  - http://arxiv.org/abs/physics/0201061
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Voss, Andreas
A1  - Malberg, Hagen
A1  - Ziehmann, Christine
A1  - Voss, Henning U.
A1  - Schirdewan, Alexander
A1  - Meyerfeldt, Udo
A1  - Kurths, Jürgen
T1  - Nonlinear analysis of complex phenomena in cardiological data
N2  - The main intention of this contribution is to discuss different nonlinear approaches to heart rate and blood pressure variability analysis for a better understanding of the cardiovascular regulation. We investigate measures of complexity which are based on symbolic dynamics, renormalised entropy and the finite time growth rates. The dual sequence method to estimate the baroreflex sensitivity and the maximal correlation method to estimate the nonlinear coupling between time series are employed for analysing bivariate data. The latter appears to be a suitable method to estimate the strength of the nonlinear coupling and the coupling direction. Heart rate and blood pressure data from clinical pilot studies and from very large clinical studies are analysed. We demonstrate that parameters from nonlinear dynamics are useful for risk stratification after myocardial infarction, for the prediction of life-threatening cardiac events even in short time series, and for modelling the relationship between heart rate and blood pressure regulation. These findings could be of importance for clinical diagnostics, in algorithms for risk stratification, and for therapeutic and preventive tools of next generation implantable cardioverter defibrillators.
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Kurths, Jürgen
A1  - Mayer-Kress, Gottfried
ED  - Kantz, Holger
T1  - Nonlinear analysis of physiological data
Y1  - 1998
SN  - 3-540-63481-9
PB  - Springer
CY  - Berlin, New York
ER  - 
TY  - JOUR
A1  - Donges, Jonathan
A1  - Donner, Reik Volker
A1  - Trauth, Martin H.
A1  - Marwan, Norbert
A1  - Schellnhuber, Hans Joachim
A1  - Kurths, Jürgen
T1  - Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution
JF  - Proceedings of the National Academy of Sciences of the United States of America
N2  - Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B. P.), (ii) Early Pleistocene (2.25-1.6 Ma B. P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B. P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
KW  - African climate
KW  - Plio-Pleistocene
KW  - climate-driven evolution
KW  - dynamical transitions
KW  - nonlinear time series analysis
Y1  - 2011
U6  - https://doi.org/10.1073/pnas.1117052108
SN  - 0027-8424
VL  - 108
IS  - 51
SP  - 20422
EP  - 20427
PB  - National Acad. of Sciences
CY  - Washington
ER  - 
TY  - JOUR
A1  - Gamez, A. J.
A1  - Zhou, Changsong
A1  - Timmermann, A.
A1  - Kurths, Jürgen
T1  - Nonlinear dimensionality reduction in climate data
N2  - Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence that makes the selection of a proper minimum number of subspaces for successfully representing the variability of the process ambiguous. The use of nonlinear methods can improve the embedding of multivariate data into lower dimensional manifolds. In this article, a nonlinear method for dimensionality reduction, Isomap, is applied to the sea surface temperature and thermocline data in the tropical Pacific Ocean, where the El Nino-Southern Oscillation (ENSO) phenomenon and the annual cycle phenomena interact. Isomap gives a more accurate description of the manifold dimensionality of the physical system. The knowledge of the minimum number of dimensions is expected to improve the development of low dimensional models for understanding and predicting ENSO
Y1  - 2004
SN  - 1023-5809
ER  - 
TY  - JOUR
A1  - Voss, Henning U.
A1  - Timmer, Jens
A1  - Kurths, Jürgen
T1  - Nonlinear dynamical system identification from uncertain and indirect measurements
N2  - We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples
Y1  - 2004
SN  - 0218-1274
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Kleiner, H. J.
A1  - Voss, Andreas
A1  - Kurths, Jürgen
A1  - Dietz, R.
T1  - Nonlinear dynamics in cardiovasscular diseases
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Scheffczyk, Christian
A1  - Engbert, Ralf
A1  - Krampe, Ralf-Thomas
A1  - Kurths, Jürgen
A1  - Rosenblum, Michael
A1  - Zaikin, Alexei A.
T1  - Nonlinear Modelling of Polyrhythmic Hand Movements
Y1  - 1996
ER  - 
TY  - JOUR
A1  - Scheffczyk, Christian
A1  - Engbert, Ralf
A1  - Kurths, Jürgen
A1  - Krampe, Ralf-Thomas
A1  - Kliegl, Reinhold
T1  - Nonlinear Phenomena in Polyrhythmic Hand Movements
N2  - In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed.
Y1  - 1995
SN  - 981-02-2689-6
ER  - 
TY  - JOUR
A1  - Zöller, Gert
A1  - Hainzl, Sebastian
A1  - Kurths, Jürgen
T1  - Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Landa, Polina S.
A1  - Zaikin, Alexei A
A1  - Kurths, Jürgen
T1  - On noise-induced transitions in nonlinear oscillators
Y1  - 2000
SN  - 3-540- 41074-0
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Park, Eun Hyoung
A1  - Kurths, Jürgen
T1  - On phase synchronization by periodic force in chaotic oscillators with saddle equilibria
Y1  - 2000
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  - 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  - INPR
A1  - Witt, Annette
A1  - Kurths, Jürgen
A1  - Krause, F.
A1  - Fischer, K.
T1  - On the validity of a model for the reversals of the Earth‘s magnetic field
N2  - We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.
T3  - NLD Preprints - 4 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13460
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Rosenblum, Michael
A1  - Landa, Polina S.
A1  - Kurths, Jürgen
T1  - On-off itermittency phenomena in a pendulum with a randomly vibrating suspension axis
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Zaikin, Alexey
A1  - Kurths, Jürgen
T1  - Optimal length transportation hypothesis to model proteasome product size distribution
JF  - Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences
N2  - This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport.
KW  - proteasome
KW  - protein translocation
KW  - stochastic process
KW  - ratchets
Y1  - 2006
U6  - https://doi.org/10.1007/s10867-006-9014-z
SN  - 0092-0606
VL  - 32
IS  - 3-4
SP  - 231
EP  - 243
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Schelter, Björn
A1  - Winterhalder, Matthias
A1  - Dahlhaus, Rainer
A1  - Kurths, Jürgen
A1  - Timmer, Jens
T1  - Partial phase synchronization for multivariate synchronizing systems
N2  - Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated
Y1  - 2006
UR  - http://prl.aps.org/abstract/PRL/v96/i20/e208103
U6  - https://doi.org/10.1103/Physrevlett.96.208103
ER  - 
TY  - GEN
A1  - Li, Yongge
A1  - Mei, Ruoxing
A1  - Xu, Yong
A1  - Kurths, Jürgen
A1  - Duan, Jinqiao
A1  - Metzler, Ralf
T1  - Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 974 
KW  - diffusion
KW  - channel
KW  - space-dependent diffusivity
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-474542
SN  - 1866-8372
IS  - 974
ER  - 
TY  - JOUR
A1  - Li, Yongge
A1  - Mei, Ruoxing
A1  - Xu, Yong
A1  - Kurths, Jürgen
A1  - Duan, Jinqiao
A1  - Metzler, Ralf
T1  - Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity
JF  - New Journal of Physics
N2  - This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.
KW  - diffusion
KW  - channel
KW  - space-dependent diffusivity
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/ab81b9
SN  - 1367-2630
VL  - 22
PB  - Dt. Physikalische Ges.
CY  - Bad Honnef
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  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization in driven and coupled chaotic oscillators
Y1  - 1997
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  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization in noisy and chaotic oscillators
Y1  - 1997
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  - JOUR
A1  - Park, Eun Hyoung
A1  - Zaks, Michael A.
A1  - Kurths, Jürgen
T1  - Phase synchronization in the forced lorenz system
Y1  - 1999
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  - 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  - 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  - 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  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Zaks, Michael A.
A1  - Kurths, Jürgen
T1  - Phase synchronization of regular and chaotic oscillators
Y1  - 1999
ER  - 
TY  - INPR
A1  - Guasti, Giovanna
A1  - Engbert, Ralf
A1  - Krampe, Ralf T.
A1  - Kurths, Jürgen
T1  - Phase transitions, complexity, and stationarity in the production of polyrhythms
N2  - Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook
T3  - NLD Preprints - 57 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14933
ER  - 
TY  - JOUR
A1  - Tokuda, I.
A1  - Kurths, Jürgen
A1  - Allaria, Eugenio
A1  - Meucci, Riccardo
A1  - Boccaletti, Stefano
A1  - Arecchi, Fortunato Tito
T1  - Predicting phase synchronization in a spiking chaotic CO2 laser
N2  - An approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2 laser from experimental data. We analyze this laser system in a regime able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as nonsynchronization in a broad parameter space of forcing frequency and amplitude without further experiments
Y1  - 2004
SN  - 1063-651X
ER  - 
TY  - JOUR
A1  - Saparin, P. I.
A1  - Thomsen, J. S.
A1  - Prohaska, Steffen
A1  - Zaikin, Alexei
A1  - Kurths, Jürgen
A1  - Hege, H. C.
A1  - Gowin, W.
T1  - Quantification of spatial structure of human proximal tibial bone biopsies using 3D measures of complexity
N2  - Changes in trabecular bone composition during development of osteoporosis are used as a model for bone loss in microgravity conditions during a space flight. Symbolic dynamics and measures of complexity are proposed and applied to assess quantitatively the structural composition of bone tissue from 3D data sets of human tibia bone biopsies acquired by a micro-CT scanner. In order to justify the newly proposed approach, the measures of complexity of the bone architecture were compared with the results of traditional 2D bone histomorphometry. The proposed technique is able to quantify the structural loss of the bone tissue and may help to diagnose and to monitor changes in bone structure of patients on Earth as well as of the space-flying personnel. © 2005 Elsevier Ltd. All rights reserved
Y1  - 2005
SN  - 0094-5765
ER  - 
TY  - JOUR
A1  - Marwan, Norbert
A1  - Beller, Gise
A1  - Felsenberg, Dieter
A1  - Saparin, Peter
A1  - Kurths, Jürgen
T1  - quantifying changes in the spatial structure of trabecular bone
JF  - International journal of bifurcation and chaos : in applied sciences and engineering
N2  - We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization.
KW  - 3D medical image analysis
KW  - pQCT
KW  - trabecular bone
KW  - patient immobilization
Y1  - 2012
U6  - https://doi.org/10.1142/S0218127412500277
SN  - 0218-1274
VL  - 22
IS  - 2
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Shabunin, A.
A1  - Astakhov, Vladimir V.
A1  - Kurths, Jürgen
T1  - Quantitative analysis of chaotic synchronization by means of coherence
N2  - We use an index of chaotic synchronization based on the averaged coherence function for the quantitative analysis of the process of the complete synchronization loss in unidirectionally coupled oscillators and maps. We demonstrate that this value manifests different stages of the synchronization breaking. It is invariant to time delay and insensitive to small noise and distortions, which can influence the accessible signals at measurements. Peculiarities of the synchronization destruction in maps and oscillators are investigated
Y1  - 2005
SN  - 1539-3755
ER  - 
TY  - INPR
A1  - Kurths, Jürgen
A1  - Voss, A.
A1  - Witt, Annette
A1  - Saparin, P.
A1  - Kleiner, H. J.
A1  - Wessel, Niels
T1  - Quantitative analysis of heart rate variability
N2  - In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.
T3  - NLD Preprints - 5 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13470
ER  - 
TY  - JOUR
A1  - Rusconi, Marco
A1  - Valleriani, Angelo
A1  - Dunlop, John William Chapman
A1  - Kurths, Jürgen
A1  - Weinkamer, Richard
T1  - Quantitative approach to the stochastics of bone remodeling
JF  - epl : a letters journal exploring the frontiers of physics
N2  - During life bones constantly adapt their structure to their mechanical environment via a mechanically controlled process called bone remodeling. For trabecular bone, this process modifies the thickness of each trabecula leading occasionally to full resorption. We describe the irreversible dynamics of the trabecular thickness distribution (TTD) by means of a Markov chain discrete in space and time. By using thickness data from adult patients, we derive the transition probabilities in the chain. This allows a quantification, in terms of geometrical quantities, of the control of bone remodeling and thus to determine the evolution of the TTD with age.
Y1  - 2012
U6  - https://doi.org/10.1209/0295-5075/97/28009
SN  - 0295-5075
VL  - 97
IS  - 2
PB  - EDP Sciences
CY  - Mulhouse
ER  - 
TY  - JOUR
A1  - Petrov, Valko
A1  - Kurths, Jürgen
A1  - Georgiev, Nikola
T1  - Reconstructing differential equation from a time series
N2  - This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient
Y1  - 2003
SN  - 0218-1274
ER  - 
TY  - INPR
A1  - Voss, Henning
A1  - Kurths, Jürgen
A1  - Schwarz, Udo
T1  - Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis
N2  - Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.
T3  - NLD Preprints - 28 
Y1  - 1996
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14083
ER  - 
TY  - JOUR
A1  - Voss, Henning U.
A1  - Kurths, Jürgen
T1  - Reconstruction of nonlinear time delay models from data by the use of optimal transformations
Y1  - 1997
ER  - 
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  - Ramos, Antonio M. T.
A1  - Builes-Jaramillo, Alejandro
A1  - Poveda, German
A1  - Goswami, Bedartha
A1  - Macau, Elbert E. N.
A1  - Kurths, Jürgen
A1  - Marwan, Norbert
T1  - Recurrence measure of conditional dependence and applications
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Herewe propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.
Y1  - 2017
U6  - https://doi.org/10.1103/PhysRevE.95.052206
SN  - 2470-0045
SN  - 2470-0053
VL  - 95
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Marwan, Norbert
A1  - Schinkel, Stefan
A1  - Kurths, Jürgen
T1  - Recurrence plots 25 years later -Gaining confidence in dynamical transitions
JF  - epl : a letters journal exploring the frontiers of physics
N2  - Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.
Y1  - 2013
U6  - https://doi.org/10.1209/0295-5075/101/20007
SN  - 0295-5075
VL  - 101
IS  - 2
PB  - EDP Sciences
CY  - Mulhouse
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Marwan, Norbert
A1  - Meyerfeldt, Udo
A1  - Schirdewan, Alexander
A1  - Kurths, Jürgen
T1  - Recurrence quantification analysis to characterise the heart rate variability before the onset of ventricular tachycardia
N2  - Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study the
Y1  - 2001
UR  - http://link.springer.de/link/service/series/0558/bibs/2199/21990295.htm
ER  - 
TY  - JOUR
A1  - Marwan, Norbert
A1  - Wessel, Niels
A1  - Meyerfeldt, Udo
A1  - Schirdewan, Alexander
A1  - Kurths, Jürgen
T1  - Recurrence-plot-based measures of complexity and its application to heart-rate-variability data
N2  - The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.
Y1  - 2002
UR  - http://arxiv.org/abs/physics/0201064
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  - Bergner, Andre
A1  - Frasca, M.
A1  - Sciuto, G.
A1  - Buscarino, A.
A1  - Ngamga, Eulalie Joelle
A1  - Fortuna, L.
A1  - Kurths, Jürgen
T1  - Remote synchronization in star networks
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism.
Y1  - 2012
U6  - https://doi.org/10.1103/PhysRevE.85.026208
SN  - 1539-3755
VL  - 85
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Schwarz, Udo
A1  - Kurths, Jürgen
A1  - Spahn, Frank
A1  - Petzschmann, Olaf
T1  - Reply on the comment of "Clustering of granular assemblies with temperature dependent restitution and under differential rotation"
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Resonant patterns in noisy active media
N2  - We investigate noise-controlled resonant response of active media to weak periodic forcing, both in excitable and oscillatory regimes. In the excitable regime, we find that noise-induced irregular wave structures can be reorganized into frequency-locked resonant patterns by weak signals with suitable frequencies. The resonance occurs due to a matching condition between the signal frequency and the noise-induced inherent time scale of the media. m:1 resonant regions similar to the Arnold tongues in frequency locking of self-sustained oscillatory media are observed. In the self-sustained oscillatory regime, noise also controls the oscillation frequency and reshapes significantly the Arnold tongues. The combination of noise and weak signal thus could provide an efficient tool to manipulate active extended systems in experiments
Y1  - 2004
SN  - 1063-651X
ER  - 
TY  - JOUR
A1  - Landa, Polina S.
A1  - Ushakov, Vladimir
A1  - Kurths, Jürgen
T1  - Rigorous theory of stochastic resonance in overdamped bistable oscillators for weak signals
JF  - Chaos, solitons & fractals : applications in science and engineering
N2  - The results of the theoretical consideration of stochastic resonance in overdamped bistable oscillators are given. These results are founded not on the model of two states as in [McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A 1989;39:4854-69], but on splitting of motion into regular and random and the rigorous solution of the Fokker-Planck equation for the random component. We show that this resonance is caused by a change, under the influence of noise, of the system's effective stiffness and damping factor contained in the equation for the regular component. For a certain value of the noise intensity the effective stiffness is minimal, and this fact causes non-monotonic change of the output signal amplitude as the noise intensity changes. It is important that the location of the minimum and its value depend essentially on the signal frequency.
Y1  - 2006
UR  - http://www.sciencedirect.com/science/journal/09600779
U6  - https://doi.org/10.1016/j.chaos.2005.08.116
SN  - 0960-0779
VL  - 30
IS  - 3
SP  - 574
EP  - 578
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - INPR
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
A1  - Scheffczyk, Christian
T1  - Roughening interfaces in deterministic dynamics
N2  - Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.
T3  - NLD Preprints - 3 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13447
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Kurths, Jürgen
A1  - Zschau, Jochen
T1  - Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Kurths, Jürgen
T1  - Self-organization of spatio-temporal earthquake clusters
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Kurths, Jürgen
T1  - Self-organized criticality model for earthquakes : Quiescence, foreshocks and aftershocks
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Winterhalder, Matthias
A1  - Schelter, B
A1  - Kurths, Jürgen
A1  - Schulze-Borthage, A
A1  - Timmer, Jens
T1  - Sensitivity and specificity of coherence and phase synchronization analysis
N2  - In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved
Y1  - 2006
UR  - http://www.sciencedirect.com/science/article/pii/S0375960106004002 ( 11.07.2011]
U6  - https://doi.org/10.1016/j.physleta.2006.03.018
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Ziehmann, Christine
A1  - Kurths, Jürgen
A1  - Meyerfeldt, Udo
A1  - Schirdewan, Alexander
A1  - Voss, Andreas
T1  - Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates
N2  - Ventricular tachycardia or fibrillation (VT-VF) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this study is to find early signs of sustained VT-VF in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they store the 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 17 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e., without a VT-VF event. To characterize these rather short data sets, we calculate heart rate variability parameters from the time and frequency domain, from symbolic dynamics as well as the finite-time growth rates. We find that neither the time nor the frequency domain parameters show significant differences between the VT-VF and the control time series. However, two parameters from symbolic dynamics as well as the finite-time growth rates discriminate significantly both groups. These findings could be of importance in algorithms for next generation ICD's to improve the diagnostics and therapy of VT-VF.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Zou, Yong
A1  - Thiel, M.
A1  - Romano, Maria Carmen
A1  - Kurths, Jürgen
A1  - Bi, Q.
T1  - Shrimp structure and associated dynamics in parametrically excited oscillators
JF  - International journal of bifurcation and chaos : in applied sciences and engineering
N2  - We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.
KW  - bifurcation analysis
KW  - recurrence plot
KW  - period doubling
KW  - intermittency
Y1  - 2006
U6  - https://doi.org/10.1142/S0218127406016987
SN  - 0218-1274
VL  - 16
IS  - 12
SP  - 3567
EP  - 3579
PB  - World Scientific Publ. Co
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Kurths, Jürgen
T1  - Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Murali, K.
A1  - Kurths, Jürgen
T1  - Simple electronic circuit model for doubly stochastic resonance
N2  - We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applications of this effect and design a simple lattice of electronic circuits for the experimental realization of doubly stochastic resonance.
Y1  - 2001
UR  - http://link.aps.org/abstract/PRE/v63/e020103
ER  - 
TY  - JOUR
A1  - Schmidt, G.
A1  - Zamora-Lopez, Gorka
A1  - Kurths, Jürgen
T1  - Simulation of large scale cortical networks by individual neuron dynamics
N2  - Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required.
Y1  - 2010
U6  - https://doi.org/10.1142/S0218127410026149
SN  - 0218-1274
ER  - 
TY  - INPR
A1  - Pikovskij, Arkadij
A1  - Zaks, Michael A.
A1  - Feudel, Ulrike
A1  - Kurths, Jürgen
T1  - Singular continuous spectra in dissipative dynamics
N2  - We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.
T3  - NLD Preprints - 15 
Y1  - 1995
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13787
ER  - 
TY  - JOUR
A1  - Feudel, Ulrike
A1  - Jansen, Wolfgang
A1  - Kurths, Jürgen
A1  - Schwarz, Udo
A1  - Voss, Henning U.
T1  - Solar variability : simple models and proxy data
Y1  - 1997
SN  - 4-274-90187-4
ER  - 
TY  - JOUR
A1  - Vasconcelos, D. B.
A1  - Lopes, S. R.
A1  - Viana, R. L.
A1  - Kurths, Jürgen
T1  - Spatial recurrence plots
N2  - We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes
Y1  - 2006
UR  - http://pre.aps.org/pdf/PRE/v73/i5/e056207
U6  - https://doi.org/10.1103/Physreve.73.056207
ER  - 
TY  - JOUR
A1  - Sun, Xiaojuan
A1  - Lu, Qishao
A1  - Kurths, Jürgen
A1  - Wang, Qingyun
T1  - Spatiotemporal coherence resonance in a map lattice
N2  - We study the effects of parametric noise on a lattice network, which is locally modeled by a two-dimensional Rulkov map. We conclude that at some intermediate noise intensity, parametric noise can induce ordered circular patterns, which indicates the appearance of spatiotemporal coherence resonance in the studied lattice. With the observation of coherence-like manner in linear spatial cross-correlation, the coherence phenomena can be analyzed quantitatively.
Y1  - 2009
UR  - http://www.worldscinet.com/ijbc/ijbc.shtml
U6  - https://doi.org/10.1142/S021812740902310X
SN  - 0218-1274
ER  - 
TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Vadivasova, T. E.
A1  - Kopeikin, A. S.
A1  - Strelkova, G. I.
A1  - Kurths, Jürgen
T1  - Spectral and correlation analysis of spiral chaos
N2  - We study numerically the behavior of the autocorrelation function (ACF) and the power spectrum of spiral attractors without and in the presence of noise. It is shown that the ACF decays exponentially and has two different time scales. The rate of the ACF decrease is defined by the amplitude fluctuations on small time intervals, i.e., when tau < tau(cor), and by the effective diffusion coefficient of the instantantaneous phase on large time intervals. it is also demonstrated that the ACF in the Poincare map also decreases according to the exponential law exp(-lambda(+)k), where lambda(+) is the positive Lyapunov exponent. The obtained results are compared with the theory of fluctuations for the Van der Pol oscillator
Y1  - 2003
SN  - 0219-4775
ER  - 
TY  - JOUR
A1  - Thiel, Marco
A1  - Romano, Maria Carmen
A1  - Kurths, Jürgen
T1  - Spurious structures in recurrence plots induced by embedding
N2  - In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay
Y1  - 2006
U6  - https://doi.org/10.1007/s11071-006-2010-9
ER  - 
TY  - JOUR
A1  - Kuznetsov, A. S.
A1  - Kurths, Jürgen
T1  - Stable heteroclinic cycles for ensembles of chaotic oscillators
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Zakharova, Anna
A1  - Vadivasova, Tatjana
A1  - Anishchenko, Vadim S.
A1  - Koseska, Aneta
A1  - Kurths, Jürgen
T1  - Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator
N2  - We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.
Y1  - 2010
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.81.011106
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Volkov, E. I.
A1  - Ullner, Ekkehard
A1  - Kurths, Jürgen
T1  - Stochastic multiresonance in the coupled relaxation oscillators
N2  - We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh- Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency. (C) 2005 American Institute of Physics
Y1  - 2005
SN  - 1054-1500
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  - Anishchenko, Vadim S.
A1  - Kopeikin, A. S.
A1  - Kurths, Jürgen
T1  - Studying hyperbolicity in chaotic systems
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Thiel, M.
A1  - Romano, Maria Carmen
A1  - Schwarz, Udo
A1  - Kurths, Jürgen
A1  - Timmer, Jens
T1  - Surrogate-based hypothesis test without surrogates
N2  - Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1
Y1  - 2004
SN  - 0218-1274
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  - Wessel, Niels
A1  - Schwarz, Udo
A1  - Saparin, Peter
A1  - Kurths, Jürgen
T1  - Symbolic dynamics for medical data analysis
N2  - Observational data of natural systems, as measured in medical measurements are typically quite different from those obtained in laboratories. Due to the peculiarities of these data, wellknown characteristics, such as power spectra or fractal dimension, often do not provide a suitable description. To study such data, we present here some measures of complexity, which are basing on symbolic dynamics. Firstly, a motivation for using symbolic dynamics and measures of complexity in data analysis based on the logistic map is given and next, two applications to medical data are shown. We demonstrate that symbolic dynamics is a useful tool for the risk assessment of patients after myocardial infarction as well as for the evaluation of th e architecture of human cancellous bone.
Y1  - 2002
UR  - http://www.agnld.uni-potsdam.de/~shw/Paper/EUROATTRACTOR2000.ps
SN  - 3-936142-09-2
ER  - 
TY  - JOUR
A1  - Engbert, Ralf
A1  - Scheffczyk, Christian
A1  - Krampe, Ralf-Thomas
A1  - Kurths, Jürgen
A1  - Kliegl, Reinhold
T1  - Symbolic dynamics of bimanual production of polyrhythms
N2  - We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system.
Y1  - 2002
SN  - 3-540- 63481-9
ER  - 
TY  - JOUR
A1  - Schiek, Michael
A1  - Scheffczyk, Christian
A1  - Engbert, Ralf
A1  - Kurths, Jürgen
A1  - Krampe, Ralf-Thomas
A1  - Kliegl, Reinhold
A1  - Drepper, Friedhelm R.
T1  - Symbolic dynamics of physiological synchronisation : examples from bimanual movements and cardiorespiratory interaction
N2  - Key words: Nonlinear time series analysis, symbolic dynamics, phase transitions, physiological data, biological synchronization, production of polyrhythms, cardiorespiratory interaction, variation of control parameter
Y1  - 1997
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  - Kurths, Jürgen
A1  - Romano, Maria Carmen
A1  - Thiel, Marco
A1  - Osipov, Grigory V.
A1  - Ivanchenko, Mikhail V.
A1  - Kiss, Istvan Z.
A1  - Hudson, John L.
T1  - Synchronization analysis of coupled noncoherent oscillators
N2  - We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators
Y1  - 2006
UR  - http://www.springerlink.com/content/102972
U6  - https://doi.org/10.1007/s11071-006-1957-x
SN  - 0924-090X
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  - Boccaletti, Stefano
A1  - Hwang, Dong-Uk
A1  - Chavez, Mario
A1  - Amann, Andreas
A1  - Kurths, Jürgen
A1  - Pecora, Louis M.
T1  - Synchronization in dynamical networks : evolution along commutative graphs
N2  - Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior
Y1  - 2006
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.74.016102
SN  - 1539-3755
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  - 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  - Huang, Tingwen
A1  - Chen, Guanrong
A1  - Kurths, Jürgen
T1  - Synchronization of chaotic of chaotic systems with time-varying coupöing delays
JF  - Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations
N2  - In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation in equalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method.
KW  - Synchronization
KW  - Chaotic System
KW  - Time-varying Delay
Y1  - 2011
U6  - https://doi.org/10.3934/dcdsb.2011.16.1071
SN  - 1531-3492
VL  - 16
IS  - 4
SP  - 1071
EP  - 1082
PB  - American Institute of Mathematical Sciences
CY  - Springfield
ER  - 
TY  - JOUR
A1  - Boccaletti, Stefano
A1  - Valladares, D. L.
A1  - Kurths, Jürgen
T1  - Synchronization of chaotic structurally nonequivalent systems
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Li, Changpin
A1  - Sun, Weigang
A1  - Kurths, Jürgen
T1  - Synchronization of complex dynamical networks with time delays
N2  - In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems.
Y1  - 2006
UR  - http://www.sciencedirect.com/science/journal/03784371
U6  - https://doi.org/10.1016/j.physa.2005.07.007
SN  - 0378-4371
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  - Montbrio, Ernest
A1  - Kurths, Jürgen
A1  - Blasius, Bernd
T1  - Synchronization of two interacting populations of oscillators
N2  - We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed.
Y1  - 2004
UR  - http://www.agnld.uni-potsdam.de/~bernd/papers/pre3.pdf
ER  -