@article{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {Testing for phase synchronization},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series},
  language  = {en}
}
@article{GamezZhouTimmermannetal.2004,
  author    = {Gamez, A. J. and Zhou, Changsong and Timmermann, A. and Kurths, J{\"u}rgen},
  title     = {Nonlinear dimensionality reduction in climate data},
  issn      = {1023-5809},
  year      = {2004},
  abstract  = {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},
  language  = {en}
}
@article{BoveBoccalettiBragardetal.2004,
  author    = {Bove, I. and Boccaletti, Stefano and Bragard, Jean and Kurths, J{\"u}rgen and Mancini, H.},
  title     = {Frequency entrainment of nonautonomous chaotic oscillators},
  year      = {2004},
  abstract  = {We give evidence of frequency entrainment of dominant peaks in the chaotic spectra of two coupled chaotic nonautonomous oscillators. At variance with the autonomous case, the phenomenon is here characterized by the vanishing of a previously positive Lyapunov exponent in the spectrum, which takes place for a broad range of the coupling strength parameter. Such a state is studied also for the case of chaotic oscillators with ill-defined phases due to the absence of a unique center of rotation. Different phase synchronization indicators are used to circumvent this difficulty},
  language  = {en}
}
@article{MaraunKurths2004,
  author    = {Maraun, Douglas and Kurths, J{\"u}rgen},
  title     = {Cross wavelet analysis: significance testing and pitfalls},
  issn      = {1023-5809},
  year      = {2004},
  abstract  = {In this paper, we present a detailed evaluation of cross wavelet analysis of bivariate time series. We develop a statistical test for zero wavelet coherency based on Monte Carlo simulations. If at least one of the two processes considered is Gaussian white noise, an approximative formula for the critical value can be utilized. In a second part, typical pitfalls of wavelet cross spectra and wavelet coherency are discussed. The wavelet cross spectrum appears to be not suitable for significance testing the interrelation between two processes. Instead, one should rather apply wavelet coherency. Furthermore we investigate problems due to multiple testing. Based on these results, we show that coherency between ENSO and NAO is an artefact for most of the time from 1900 to 1995. However, during a distinct period from around 1920 to 1940, significant coherency between the two phenomena occurs},
  language  = {en}
}
@article{RomanoThielKurthsetal.2004,
  author    = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and von Bloh, Werner},
  title     = {Multivariate recurrence plots},
  issn      = {0375-9601},
  year      = {2004},
  abstract  = {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},
  language  = {en}
}
@article{ThielRomanoSchwarzetal.2004,
  author    = {Thiel, M. and Romano, Maria Carmen and Schwarz, Udo and Kurths, J{\"u}rgen and Timmer, Jens},
  title     = {Surrogate-based hypothesis test without surrogates},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {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},
  language  = {en}
}
@article{VossTimmerKurths2004,
  author    = {Voss, Henning U. and Timmer, Jens and Kurths, J{\"u}rgen},
  title     = {Nonlinear dynamical system identification from uncertain and indirect measurements},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {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},
  language  = {en}
}
@article{ZhouKurths2004,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Resonant patterns in noisy active media},
  issn      = {1063-651X},
  year      = {2004},
  abstract  = {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},
  language  = {en}
}
@article{TokudaKurthsAllariaetal.2004,
  author    = {Tokuda, I. and Kurths, J{\"u}rgen and Allaria, Eugenio and Meucci, Riccardo and Boccaletti, Stefano and Arecchi, Fortunato Tito},
  title     = {Predicting phase synchronization in a spiking chaotic CO2 laser},
  issn      = {1063-651X},
  year      = {2004},
  abstract  = {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},
  language  = {en}
}
@article{ThielRomanoKurths2004,
  author    = {Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen},
  title     = {How much information is contained in a recurrence plot?},
  issn      = {0375-9601},
  year      = {2004},
  abstract  = {Recurrence plots have recently been recognized as a powerful tool for the analysis of data. Not only the visualization of structures of the time series but also the possibility to estimate invariants from them and the possibility to analyze non-stationary data sets are remarkable. However, the question of how much information is encoded in such a two-dimensional and binary representation has not been discussed so far. In this Letter we show that-under some conditions-it is possible to reconstruct an attractor from the recurrence plot, at least topologically. This means that all relevant dynamical information is contained in the plot. (C) 2004 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{ThielRomanoReadetal.2004,
  author    = {Thiel, M. and Romano, Maria Carmen and Read, P. L. and Kurths, J{\"u}rgen},
  title     = {Estimation of dynamical invariants without embedding by recurrence plots},
  issn      = {1054-1500},
  year      = {2004},
  abstract  = {In this paper we show that two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay. This fact is interesting as these quantities are even invariant if no embedding is used. This is an important advantage of RPs compared to other techniques of nonlinear data analysis. These estimates for the correlation dimension and entropy are robust and, moreover, can be obtained at a low numerical cost. We exemplify our results for the Rossler system, the funnel attractor and the Mackey-Glass system. In the last part of the paper we estimate dynamical invariants for data from some fluid dynamical experiments and confirm previous evidence for low dimensional chaos in this experimental system. (C) 2004 American Institute of Physics},
  language  = {en}
}
@article{AnishchenkoVadivasovaKopeikinetal.2003,
  author    = {Anishchenko, Vadim S. and Vadivasova, T. E. and Kopeikin, A. S. and Strelkova, G. I. and Kurths, J{\"u}rgen},
  title     = {Spectral and correlation analysis of spiral chaos},
  issn      = {0219-4775},
  year      = {2003},
  abstract  = {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},
  language  = {en}
}
@article{PetrovKurthsGeorgiev2003,
  author    = {Petrov, Valko and Kurths, J{\"u}rgen and Georgiev, Nikola},
  title     = {Reconstructing differential equation from a time series},
  issn      = {0218-1274},
  year      = {2003},
  abstract  = {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},
  language  = {en}
}
@article{SteuerZhouKurths2003,
  author    = {Steuer, Ralf and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Constructive effects of fluctuations in genetic and biochemical regulatory systems},
  issn      = {0303-2647},
  year      = {2003},
  abstract  = {Biochemical and genetic regulatory systems that involve low concentrations of molecules are inherently noisy. This intrinsic stochasticity, has received considerable interest recently, leading to new insights about the sources and consequences of noise in complex systems of genetic regulation. However, most prior work was devoted to the reduction of fluctuation and the robustness of cellular function with respect to intrinsic noise. Here, we focus on several scenarios in which the inherent molecular fluctuations are not merely a nuisance, but act constructively and bring about qualitative changes in the dynamics of the system. It will be demonstrated that in many typical situations biochemical and genetic regulatory systems may utilize intrinsic noise to their advantage. (C) 2002 Elsevier Ireland Ltd. All rights reserved},
  language  = {en}
}
@article{SteuerKurthsFiehnetal.2003,
  author    = {Steuer, Ralf and Kurths, J{\"u}rgen and Fiehn, Oliver and Weckwerth, Wolfram},
  title     = {Interpreting correlations in metabolomic networks},
  issn      = {0300-5127},
  year      = {2003},
  abstract  = {Correlations, as observed between the concentrations of metabolites in a biological sample, may be used to gain additional information about the physiological state of a given tissue. in this mini-review, we discuss the integration of these observed correlations into metabolomic networks and their relationships with the underlying biochemical pathways},
  language  = {en}
}
@article{VianaGrebogiPintoetal.2003,
  author    = {Viana, R. L. and Grebogi, Celso and Pinto, Seds and Lopes, S. R. and Batista, A. M. and Kurths, J{\"u}rgen},
  title     = {Validity of numerical trajectories in the synchronization transition of complex systems},
  issn      = {1063-651X},
  year      = {2003},
  abstract  = {We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties},
  language  = {en}
}
@article{VolkovUllnerZaikinetal.2003,
  author    = {Volkov, E. I. and Ullner, Ekkehard and Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Frequency-dependent stochastic resonance in inhibitory coupled excitable systems},
  issn      = {1063-651X},
  year      = {2003},
  abstract  = {We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise- supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations},
  language  = {en}
}
@article{WesselSchwarzSaparinetal.2002,
  author    = {Wessel, Niels and Schwarz, Udo and Saparin, Peter and Kurths, J{\"u}rgen},
  title     = {Symbolic dynamics for medical data analysis},
  isbn      = {3-936142-09-2},
  year      = {2002},
  abstract  = {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.},
  language  = {en}
}
@article{BaltanasZaikinFeudeletal.2002,
  author    = {Baltan{\´a}s, J. P. and Zaikin, Alexei A. and Feudel, Fred and Kurths, J{\"u}rgen and Sanjuan, Miguel Angel Fern{\´a}ndez},
  title     = {Noise-induced effects in tracer dynamics},
  year      = {2002},
  language  = {en}
}
@article{ZaikinGarciaOjalvoSchimanskyGeieretal.2002,
  author    = {Zaikin, Alexei A. and Garc{\´i}a-Ojalvo, Jordi and Schimansky-Geier, Lutz and Kurths, J{\"u}rgen},
  title     = {Noise induced propagation in monostable media},
  year      = {2002},
  abstract  = {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.},
  language  = {en}
}
@article{ZaikinLopezBaltanasetal.2002,
  author    = {Zaikin, Alexei A. and L{\´o}pez, L and Baltan{\´a}s, J. P. and Kurths, J{\"u}rgen and Sanjuan, Miguel Angel Fern{\´a}ndez},
  title     = {Vibrational resonance in noise-induced structure},
  year      = {2002},
  abstract  = {We report on the effect of vibrational resonance in a spatially extended system of coupled noisy oscillators under the action of two periodic forces, a low-frequency one (signal) and a high-frequency one (carrier). Vibrational resonance manifests itself in the fact that for optimally selected values of high-frequency force amplitude, the response of the system to a low-frequency signal is optimal. This phenomenon is a synthesis of two effects, a noise- induced phase transition leading to bistability, and a conventional vibrational resonance, resulting in the optimization of signal processing. Numerical simulations, which demonstrate this effect for an extended system, can be understood by means of a zero-dimensional "effective" model. The behavior of this "effective" model is also confirmed by an experimental realization of an electronic circuit.},
  language  = {en}
}
@article{SitzSchwarzKurthsetal.2002,
  author    = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen and Voss, Henning U.},
  title     = {Estimation of parameters and unobserved components for nonlinear systems from noisy time series},
  year      = {2002},
  abstract  = {We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data.},
  language  = {en}
}
@unpublished{WittNeimanKurths1997,
  author    = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen},
  title     = {Characterizing the dynamics of stochastic bistable systems by measures of complexity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14556},
  year      = {1997},
  abstract  = {The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.},
  language  = {en}
}
@misc{KoseskaZaikinKurthsetal.2009,
  author    = {Koseska, Aneta and Zaikin, Alexey and Kurths, J{\"u}rgen and Garc{\´i}a-Ojalvo, Jordi},
  title     = {Timing cellular decision making under noise via cell-cell communication},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-45260},
  year      = {2009},
  abstract  = {Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact.},
  language  = {en}
}
@unpublished{WittKurthsKrauseetal.1994,
  author    = {Witt, Annette and Kurths, J{\"u}rgen and Krause, F. and Fischer, K.},
  title     = {On the validity of a model for the reversals of the Earth's magnetic field},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13460},
  year      = {1994},
  abstract  = {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.},
  language  = {en}
}
@unpublished{KurthsVossWittetal.1994,
  author    = {Kurths, J{\"u}rgen and Voss, A. and Witt, Annette and Saparin, P. and Kleiner, H. J. and Wessel, Niels},
  title     = {Quantitative analysis of heart rate variability},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13470},
  year      = {1994},
  abstract  = {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.},
  language  = {en}
}
@unpublished{ThiessenhusenEspositoKurthsetal.1995,
  author    = {Thiessenhusen, Kai-Uwe and Esposito, Larry W. and Kurths, J{\"u}rgen and Spahn, Frank},
  title     = {Detection of hidden resonances in Saturn's B-ring},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13618},
  year      = {1995},
  abstract  = {The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.},
  language  = {en}
}
@unpublished{VossKurthsSchwarz1996,
  author    = {Voss, Henning and Kurths, J{\"u}rgen and Schwarz, Udo},
  title     = {Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14083},
  year      = {1996},
  abstract  = {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.},
  language  = {en}
}
@article{PalusKurthsSchwarzetal.2007,
  author    = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Seehafer, Norbert and Novotna, Dagmar and Charvatova, Ivanka},
  title     = {The solar activity cycle is weakly synchronized with the solar inertial motion},
  doi       = {10.1016/j.physleta.2007.01.039},
  year      = {2007},
  abstract  = {We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM.},
  language  = {en}
}
@article{KurthsSeehaferSpahn1999,
  author    = {Kurths, J{\"u}rgen and Seehafer, Norbert and Spahn, Frank},
  title     = {Nichtlineare Dynamik in der Physik : Forschungsbeispiele und Forschungstrends},
  isbn      = {3-540-65329- 5},
  year      = {1999},
  language  = {de}
}
@misc{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {Testing for phase synchronization},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20091},
  year      = {2004},
  abstract  = {We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-samples test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.},
  language  = {en}
}
@misc{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {An approach to multivariate phase synchronization analysis and its application to event-related potentials},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20106},
  year      = {2004},
  abstract  = {A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.},
  language  = {en}
}
@unpublished{GuastiEngbertKrampeetal.2000,
  author    = {Guasti, Giovanna and Engbert, Ralf and Krampe, Ralf T. and Kurths, J{\"u}rgen},
  title     = {Phase transitions, complexity, and stationarity in the production of polyrhythms},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14933},
  year      = {2000},
  abstract  = {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},
  language  = {en}
}
@misc{LiMeiXuetal.2020,
  author    = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf},
  title     = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {974},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47454},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-474542},
  pages     = {28},
  year      = {2020},
  abstract  = {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 It{\^o} 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.},
  language  = {en}
}
@article{LiMeiXuetal.2020,
  author    = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf},
  title     = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity},
  series = {New Journal of Physics},
  volume    = {22},
  journal   = {New Journal of Physics},
  publisher = {Dt. Physikalische Ges.},
  address   = {Bad Honnef},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab81b9},
  pages     = {27},
  year      = {2020},
  abstract  = {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 It{\^o} 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.},
  language  = {en}
}
@article{ScheffczykEngbertKrampeetal.1996,
  author    = {Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen and Rosenblum, Michael and Zaikin, Alexei A.},
  title     = {Nonlinear Modelling of Polyrhythmic Hand Movements},
  year      = {1996},
  language  = {en}
}
@article{KomalapriyaRomanoBlascoThieletal.2009,
  author    = {Komalapriya, Chandrasekaran and Romano Blasco, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Simonotto, Jennifer and Furman, Michael and Ditto, William L. and Carney, Paul R.},
  title     = {Analysis of high-resulution microelectrode EEG recordings in an animal model of spontaneous limbic seizures},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127409023226},
  year      = {2009},
  language  = {en}
}
@article{SureshSenthilkumarLakshmananetal.2010,
  author    = {Suresh, R. and Senthilkumar, Dharmapuri Vijayan and Lakshmanan, Muthusamy and Kurths, J{\"u}rgen},
  title     = {Global phase synchronization in an array of time-delay systems},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.82.016215},
  year      = {2010},
  abstract  = {We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.},
  language  = {en}
}
@article{SchelterWinterhalderDahlhausetal.2006,
  author    = {Schelter, Bj{\"o}rn and Winterhalder, Matthias and Dahlhaus, Rainer and Kurths, J{\"u}rgen and Timmer, Jens},
  title     = {Partial phase synchronization for multivariate synchronizing systems},
  doi       = {10.1103/Physrevlett.96.208103},
  year      = {2006},
  abstract  = {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},
  language  = {en}
}
@article{ZhouKurths2006,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Dynamical weights and enhanced synchronization in adaptive complex networks},
  doi       = {10.1103/Physrevlett.96.164102},
  year      = {2006},
  abstract  = {Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks},
  language  = {en}
}
@article{ZhouMotterKurths2006,
  author    = {Zhou, Changsong and Motter, Adilson E. and Kurths, J{\"u}rgen},
  title     = {Universality in the synchronization of weighted random networks},
  doi       = {10.1103/Physrevlett.96.034101},
  year      = {2006},
  abstract  = {Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters},
  language  = {en}
}
@article{LiChenWuetal.2009,
  author    = {Li, Ping and Chen, Maoyin and Wu, Ye and Kurths, J{\"u}rgen},
  title     = {Matrix-measure criterion for synchronization in coupled-map networks},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.79.067102},
  year      = {2009},
  abstract  = {We present conditions for the local and global synchronizations in coupled-map networks using the matrix measure approach. In contrast to many existing synchronization conditions, the proposed synchronization criteria do not depend on the solution of the synchronous state and give less limitation on the network connections. Numerical simulations of the coupled quadratic maps demonstrate the potentials of our main results.},
  language  = {en}
}
@article{KliemSchwarzKurthsetal.1998,
  author    = {Kliem, Bernhard and Schwarz, Udo and Kurths, J{\"u}rgen and Dennis, Brian and Schwartz, Richard and Aschwanden, Markus J.},
  title     = {Wavelet analysis of solar flare hard X-ray},
  issn      = {0004-637x},
  year      = {1998},
  language  = {en}
}
@article{ZaikinRosenblumLandaetal.1998,
  author    = {Zaikin, Alexei A. and Rosenblum, Michael and Landa, Polina S. and Kurths, J{\"u}rgen},
  title     = {On-off itermittency phenomena in a pendulum with a randomly vibrating suspension axis},
  year      = {1998},
  language  = {en}
}
@article{EngbertHainzlZoelleretal.1998,
  author    = {Engbert, Ralf and Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen},
  title     = {Testing for unstable periodic orbits to characterize spatiotemporal dynamics},
  year      = {1998},
  language  = {en}
}
@article{SchwarzKurthsSpahnetal.1998,
  author    = {Schwarz, Udo and Kurths, J{\"u}rgen and Spahn, Frank and Petzschmann, Olaf},
  title     = {Reply on the comment of "Clustering of granular assemblies with temperature dependent restitution and under differential rotation"},
  year      = {1998},
  language  = {en}
}
@article{KurthsKliemSchwarzetal.1998,
  author    = {Kurths, J{\"u}rgen and Kliem, Bernhard and Schwarz, Udo and Kr{\"u}ger, Albrecht and Urpo, S.},
  title     = {Multiresolution analysis of solar mm-wave bursts},
  year      = {1998},
  language  = {en}
}
@article{KimKurthsKimetal.1998,
  author    = {Kim, G. G. and Kurths, J{\"u}rgen and Kim, S. and Cao, L. Y.},
  title     = {Detecting determinism in human posture control data},
  year      = {1998},
  language  = {en}
}
@article{RosenblumKurthsSchaeferetal.1998,
  author    = {Rosenblum, Michael and Kurths, J{\"u}rgen and Sch{\"a}fer, Carsten and Abel, Hans-Henning},
  title     = {Heartbeat synchronized with ventilation},
  year      = {1998},
  language  = {en}
}
@article{HnatkovaVesselVossetal.1998,
  author    = {Hnatkova, Katarina and Vessel, N. and Voss, Andreas and Kurths, J{\"u}rgen and Sander, A. and Schirdewan, Alexander and Camm, A. J. and Malik, Marek},
  title     = {Multiparametric analysis of heart rate variability used for risk stratification among survivors of acute myocardial infarction},
  issn      = {0895-2795},
  year      = {1998},
  language  = {en}
}