@article{WesselRiedlKurths2009, author = {Wessel, Niels and Riedl, Maik and Kurths, J{\"u}rgen}, title = {Is the normal heart rate "chaotic" due to respiration?}, issn = {1054-1500}, doi = {10.1063/1.3133128}, year = {2009}, abstract = {The incidence of cardiovascular diseases increases with the growth of the human population and an aging society, leading to very high expenses in the public health system. Therefore, it is challenging to develop sophisticated methods in order to improve medical diagnostics. The question whether the normal heart rate is chaotic or not is an attempt to elucidate the underlying mechanisms of cardiovascular dynamics and therefore a highly controversial topical challenge. In this contribution we demonstrate that linear and nonlinear parameters allow us to separate completely the data sets of the three groups provided for this controversial topic in nonlinear dynamics. The question whether these time series are chaotic or not cannot be answered satisfactorily without investigating the underlying mechanisms leading to them. We give an example of the dominant influence of respiration on heart beat dynamics, which shows that observed fluctuations can be mostly explained by respiratory modulations of heart rate and blood pressure (coefficient of determination: 96\%). Therefore, we recommend reformulating the following initial question: "Is the normal heart rate chaotic?" We rather ask the following: " Is the normal heart rate 'chaotic' due to respiration?"}, language = {en} } @article{PalusKurthsSchwarzetal.2001, author = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Novotn{\´a}, Dagmar and Charv{\´a}tov{\´a}, Ivanka}, title = {Is the solar activity cycle synchronized with the solar inertial motion?}, year = {2001}, abstract = {The 300 year record of the yearly sunspot numbers and numerically generated trajectory of the solar inertial motion (SIM) were subjects of a synchronization analysis. Phase synchronization of the sunspot cycle and a fast component of the SIM have been found and confirmed with statistical significance in three epochs (1727-1757, 1802-1832 and 1863-1922) of the entire 1700-1997 record. This result can be considered as a quantitative support for the hypothesis that there is a weak interaction of gravity and solar activity.}, language = {en} } @article{KrampeEngbertKliegletal.2000, author = {Krampe, Ralf-Thomas and Engbert, Ralf and Kliegl, Reinhold and Kurths, J{\"u}rgen}, title = {Koordination und Synchronisation der H{\"a}nde beim rhythmischen Timing}, year = {2000}, language = {de} } @article{RaabWesselSchirdewanetal.2006, author = {Raab, Corinna and Wessel, Niels and Schirdewan, Alexander and Kurths, J{\"u}rgen}, title = {Large-scale dimension densities for heart rate variability analysis}, issn = {1539-3755}, doi = {10.1103/Physreve.73.041907}, year = {2006}, abstract = {In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification}, language = {en} } @article{TokudaKurthsRosa2002, author = {Tokuda, I. and Kurths, J{\"u}rgen and Rosa, Epaminondas}, title = {Learning phase synchronization from nonsynchronized chaotic regimes}, year = {2002}, language = {en} } @article{SchwarzSpahnGrebogietal.1999, author = {Schwarz, Udo and Spahn, Frank and Grebogi, Celso and Kurths, J{\"u}rgen and Petzschmann, Olaf}, title = {Length scales of clustering in granular gases}, year = {1999}, language = {en} } @article{BraunDitlevsenKurthsetal.2010, author = {Braun, Holger and Ditlevsen, Peter D. and Kurths, J{\"u}rgen and Mudelsee, Manfred}, title = {Limitations of red noise in analysing Dansgaard-Oeschger events}, issn = {1814-9324}, doi = {10.5194/cp-6-85-2010}, year = {2010}, abstract = {During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99\%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions.}, language = {en} } @article{MarwanKurths2005, author = {Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Line structures in recurrence plots}, issn = {0375-9601}, year = {2005}, abstract = {Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occurring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time- transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements. (C) 2005 Elsevier B.V. All rights reserved}, language = {en} } @article{TimmerSchwarzVossetal.2000, author = {Timmer, Jens and Schwarz, Udo and Voss, Henning U. and Wardinski, Ingo and Belloni, Tomaso and Hasinger, G{\"u}nther and VanDerKlis, Michael and Kurths, J{\"u}rgen}, title = {Linear and Nonlinear Time Series Analysis of the Black Hole Candidate Cygnus X-1}, year = {2000}, abstract = {We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.}, language = {en} } @article{ZiehmannSmithKurths2000, author = {Ziehmann, Christine and Smith, Leonard A. and Kurths, J{\"u}rgen}, title = {Localized Lyapunov exponents and the prediction of predictability}, year = {2000}, language = {en} } @article{RosenblumPikovskijKurthsetal.2002, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen and Osipov, Grigory V. and Kiss, Istvan Z. and Hudson, J. L.}, title = {Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics}, year = {2002}, language = {en} } @article{ZolotovaPonyavinMarwanetal.2009, author = {Zolotova, Nadezhda V. and Ponyavin, Dmitri I. and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Long-term asymmetry in the wings of the butterfly diagram}, issn = {0004-6361}, doi = {10.1051/0004-6361/200811430}, year = {2009}, abstract = {Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.}, 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{GowinKurthsSaparinetal.1997, author = {Gowin, W. and Kurths, J{\"u}rgen and Saparin, Peter and Felsenberg, D.}, title = {Measures of complexity and processing of vertebral CT-images}, isbn = {0-7803-4262-3}, year = {1997}, language = {en} } @article{MeineckeZieheKurthsetal.2005, author = {Meinecke, Frank C. and Ziehe, Andreas and Kurths, J{\"u}rgen and M{\"u}ller, Klaus-Robert}, title = {Measuring phase synchronization of superimposed signals}, issn = {0031-9007}, year = {2005}, abstract = {Phase synchronization is an important phenomenon that occurs in a wide variety of complex oscillatory processes. Measuring phase synchronization can therefore help to gain fundamental insight into nature. In this Letter we point out that synchronization analysis techniques can detect spurious synchronization, if they are fed with a superposition of signals such as in electroencephalography or magnetoencephalography data. We show how techniques from blind source separation can help to nevertheless measure the true synchronization and avoid such pitfalls}, language = {en} } @article{VossTimmerKurths2004, author = {Voss, Henning U. and Timmer, Jens and Kurths, J{\"u}rgen}, title = {Modeling and identification of nonlinear systems}, issn = {0218-1274}, year = {2004}, language = {en} } @article{ZaikinKurthsSaparinetal.2005, author = {Zaikin, Alexei and Kurths, J{\"u}rgen and Saparin, Peter and Gowin, W. and Prohaska, Steffen}, title = {Modeling bone resorption in 2D CT and 3D mu CT images}, issn = {0218-1274}, year = {2005}, abstract = {We study several algorithms to simulate bone mass loss in two-dimensional and three-dimensional computed tomography bone images. The aim is to extrapolate and predict the bone loss, to provide test objects for newly developed structural measures, and to understand the physical mechanisms behind the bone alteration. Our bone model approach differs from those already reported in the literature by two features. First, we work with original bone images, obtained by computed tomography (CT); second, we use structural measures of complexity to evaluate bone resorption and to compare it with the data provided by CT. This gives us the possibility to test algorithms of bone resorption by comparing their results with experimentally found dependencies of structural measures of complexity, as well as to show efficiency of the complexity measures in the analysis of bone models. For two-dimensional images we suggest two algorithms, a threshold algorithm and a virtual slicing algorithm. The threshold algorithm simulates bone resorption on a boundary between bone and marrow, representing an activity of osteoclasts. The virtual slicing algorithm uses a distribution of the bone material between several virtually created slices to achieve statistically correct results, when the bone-marrow transition is not clearly defined. These algorithms have been tested for original CT 10 mm thick vertebral slices and for simulated 10 mm thick slices constructed from ten I mm thick slices. For three-dimensional data, we suggest a variation of the threshold algorithm and apply it to bone images. The results of modeling have been compared with CT images using structural measures of complexity in two- and three-dimensions. This comparison has confirmed credibility of a virtual slicing modeling algorithm for two-dimensional data and a threshold algorithm for three-dimensional data}, language = {en} } @article{ZaikinKurths1999, author = {Zaikin, Alexei A. and Kurths, J{\"u}rgen}, title = {Modeling Cognitive Control in Simple Movements}, isbn = {1-563-96863-0}, year = {1999}, language = {en} } @article{LaiGrebogiKurths1999, author = {Lai, Ying Cheng and Grebogi, Celso and Kurths, J{\"u}rgen}, title = {Modeling of deterministic chaotic systems}, year = {1999}, language = {en} } @article{ZaikinRosenblumScheffczyketal.1997, author = {Zaikin, Alexei A. and Rosenblum, Michael and Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen}, title = {Modeling qualitative changes in bimanual movements}, year = {1997}, language = {en} } @article{WesselAssmusWeidermannetal.2004, author = {Wessel, Niels and Aßmus, Joerg and Weidermann, Frank and Konvicka, Jan and Nestmann, S. and Neugebauer, R. and Schwarz, Udo and Kurths, J{\"u}rgen}, title = {Modeling thermal displacements in modular tool systems}, year = {2004}, abstract = {In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally induced errors can be estimated with 1-2\${mu m}\$ accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.}, language = {en} } @misc{AgarwalMarwanMaheswaranetal.2017, author = {Agarwal, Ankit and Marwan, Norbert and Maheswaran, Rathinasamy and Merz, Bruno and Kurths, J{\"u}rgen}, title = {Multi-scale event synchronization analysis for unravelling climate processes}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {661}, issn = {1866-8372}, doi = {10.25932/publishup-41827}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-418274}, pages = {13}, year = {2017}, abstract = {The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales.}, language = {en} } @article{AgarwalMarwanMaheswaranetal.2017, author = {Agarwal, Ankit and Marwan, Norbert and Maheswaran, Rathinasamy and Merz, Bruno and Kurths, J{\"u}rgen}, title = {Multi-scale event synchronization analysis for unravelling climate processes: a wavelet-based approach}, series = {Nonlinear processes in geophysics}, volume = {24}, journal = {Nonlinear processes in geophysics}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1023-5809}, doi = {10.5194/npg-24-599-2017}, pages = {599 -- 611}, year = {2017}, abstract = {The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales.}, 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} } @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{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{MotterZhouKurths2005, author = {Motter, Adilson E. and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Network synchronization, diffusion, and the paradox of heterogeneity}, issn = {1063-651X}, year = {2005}, abstract = {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}, 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} } @article{KurthsSchwarz2001, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Nichtlineare Wissenschaften - neue Paradigmen und Konzepte}, issn = {0177- 3674}, year = {2001}, abstract = {In den letzten 2 Jahrzehnten des 20. Jahrhunderts hat sich mit der rasanten Entwicklung der Nichtlinearen Wissenschaften ein weiterer Umbruch vollzogen, der eine ausgepraegte Nachhaltigkeit in Wissenschaft und Technik ebenso wie in der Gesellschaft erwarten laesst. Die Nichtlinearen Wissenschaften werden auch als Nichtlineare Dynamik, Wissenschaft Komplexer Systeme oder etwas eingegrenzt Chaostheorie bezeichnet.}, language = {de} } @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{ZhouKurthsKissetal.2002, author = {Zhou, Changsong and Kurths, J{\"u}rgen and Kiss, Istvan Z. and Hudson, J. L.}, title = {Noise-enhanced phase synchronization of chaotic oscillators}, year = {2002}, 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{ZhouKurths2002, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Noise-induced phase synchronization and synchronization transitions in chaotic oscillators}, year = {2002}, language = {en} } @article{ZhouKurths2005, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Noise-sustained and controlled synchronization of stirred excitable media by external forcing}, issn = {1367-2630}, year = {2005}, abstract = {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}, language = {en} } @article{KurthsSchwarzWitt1995, author = {Kurths, J{\"u}rgen and Schwarz, Udo and Witt, Annette}, title = {Non-linear data analysis in solar radio astronomy}, year = {1995}, abstract = {We have discussed some tools from nonlinear dynamics which may help to analyze transient phenomena, such as solar bursts. The structure function known from turbulence theory is an appropriate method to find out some scaling behavior of fluctuations in time. More generally, the wavelet analysis, which is some generalization of the power spectrum, exhibits information on the location as well as the size of hidden characteristic features. Applying both techniques to microwave bursts, we have found some scaling properties that refer to the existence of hierarchic time structures. This is in good accordance with the electric circuit model for describing the flare-particle energization process.}, language = {en} } @article{RheinwaltBoersMarwanetal.2016, author = {Rheinwalt, Aljoscha and Boers, Niklas and Marwan, Norbert and Kurths, J{\"u}rgen and Hoffmann, Peter and Gerstengarbe, Friedrich-Wilhelm and Werner, Peter}, title = {Non-linear time series analysis of precipitation events using regional climate networks for Germany}, series = {Climate dynamics : observational, theoretical and computational research on the climate system}, volume = {46}, journal = {Climate dynamics : observational, theoretical and computational research on the climate system}, publisher = {Springer}, address = {New York}, issn = {0930-7575}, doi = {10.1007/s00382-015-2632-z}, pages = {1065 -- 1074}, year = {2016}, abstract = {Synchronous occurrences of heavy rainfall events and the study of their relation in time and space are of large socio-economical relevance, for instance for the agricultural and insurance sectors, but also for the general well-being of the population. In this study, the spatial synchronization structure is analyzed as a regional climate network constructed from precipitation event series. The similarity between event series is determined by the number of synchronous occurrences. We propose a novel standardization of this number that results in synchronization scores which are not biased by the number of events in the respective time series. Additionally, we introduce a new version of the network measure directionality that measures the spatial directionality of weighted links by also taking account of the effects of the spatial embedding of the network. This measure provides an estimate of heavy precipitation isochrones by pointing out directions along which rainfall events synchronize. We propose a climatological interpretation of this measure in terms of propagating fronts or event traces and confirm it for Germany by comparing our results to known atmospheric circulation patterns.}, language = {en} } @article{BaptistaPereiraSartorellietal.2005, author = {Baptista, Murilo da Silva and Pereira, Tiago and Sartorelli, J. C. and Caldas, Ibere Luiz and Kurths, J{\"u}rgen}, title = {Non-transitive maps in phase synchronization}, year = {2005}, abstract = {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}, language = {en} } @article{MarwanKurths2001, author = {Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Nonlinear analysis of bivariate data with cross recurrence plots}, year = {2001}, abstract = {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.}, language = {en} } @article{WesselVossMalbergetal.2000, author = {Wessel, Niels and Voss, Andreas and Malberg, Hagen and Ziehmann, Christine and Voss, Henning U. and Schirdewan, Alexander and Meyerfeldt, Udo and Kurths, J{\"u}rgen}, title = {Nonlinear analysis of complex phenomena in cardiological data}, year = {2000}, abstract = {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.}, language = {en} } @book{KurthsMayerKress1998, author = {Kurths, J{\"u}rgen and Mayer-Kress, Gottfried}, title = {Nonlinear analysis of physiological data}, editor = {Kantz, Holger}, publisher = {Springer}, address = {Berlin, New York}, isbn = {3-540-63481-9}, pages = {VIII, 344 S. : Ill., graph. Darst.}, year = {1998}, language = {en} } @article{DongesDonnerTrauthetal.2011, author = {Donges, Jonathan and Donner, Reik Volker and Trauth, Martin H. and Marwan, Norbert and Schellnhuber, Hans Joachim and Kurths, J{\"u}rgen}, title = {Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution}, series = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {108}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {51}, publisher = {National Acad. of Sciences}, address = {Washington}, issn = {0027-8424}, doi = {10.1073/pnas.1117052108}, pages = {20422 -- 20427}, year = {2011}, abstract = {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.}, 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{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{WesselKleinerVossetal.1997, author = {Wessel, Niels and Kleiner, H. J. and Voss, Andreas and Kurths, J{\"u}rgen and Dietz, R.}, title = {Nonlinear dynamics in cardiovasscular diseases}, year = {1997}, 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{ScheffczykEngbertKurthsetal.1995, author = {Scheffczyk, Christian and Engbert, Ralf and Kurths, J{\"u}rgen and Krampe, Ralf-Thomas and Kliegl, Reinhold}, title = {Nonlinear Phenomena in Polyrhythmic Hand Movements}, isbn = {981-02-2689-6}, year = {1995}, abstract = {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.}, language = {en} } @article{ThielRomanoSchwarzetal.2001, author = {Thiel, Marco and Romano, Maria Carmen and Schwarz, Udo and Kurths, J{\"u}rgen and Hasinger, G{\"u}nther and Belloni, Tomaso}, title = {Nonlinear Time series analysis of the X-ray flux of compact objects}, issn = {0004-640x}, year = {2001}, abstract = {We analyse the X-ray light curves of compact objects using linear and nonlinear time series analysis methods. A Power Density Spectrum (PDS) describes the overall second order properties of the observed data well. To look beyond we propose the nonlinear Q-statistic to detect an asymmetry of the time series. This allows us to find relevant time scales. This method even grants a subclassification of the known states of X-ray sources.}, language = {en} } @article{ZoellerHainzlKurths2001, author = {Z{\"o}ller, Gert and Hainzl, Sebastian and Kurths, J{\"u}rgen}, title = {Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes}, year = {2001}, language = {en} } @article{LandaZaikinKurths2000, author = {Landa, Polina S. and Zaikin, Alexei A and Kurths, J{\"u}rgen}, title = {On noise-induced transitions in nonlinear oscillators}, isbn = {3-540- 41074-0}, year = {2000}, language = {en} } @article{ZaksParkKurths2000, author = {Zaks, Michael A. and Park, Eun Hyoung and Kurths, J{\"u}rgen}, title = {On phase synchronization by periodic force in chaotic oscillators with saddle equilibria}, year = {2000}, language = {en} } @article{ZaksPikovskijKurths1997, author = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {On the correlation dimension of the spectral measure for the Thue-Morse sequence}, year = {1997}, language = {en} } @article{BittmannGutschowLutheretal.2005, author = {Bittmann, Frank and Gutschow, Stephan and Luther, Sven and Wessel, Niels and Kurths, J{\"u}rgen}, title = {On the functional relationship between postural motor balance and performance at school}, year = {2005}, abstract = {In integrated medical considerations of the biological human system, both intellectual and motor performances in a similar manner are considered as a result of the function of the nervous system. Consequently, universal minimal dysfunctions of the central nervous system may lead to both intellectual and physical anomalies. Therefore, this study tests the hypothesis that there is a connection between the balance ability as a motor parameter and school success as an intellectual parameter. A postural measuring system based on the force-moment sensor technique was used to record the postural balance regulation of 773 children (circle divide 11 +/- 1 years). The school achievement of each child was determined by school grades. Data analysis was performed by linear as well as by nonlinear time series analyses. There are highly significant differences in balance regulation between good and poor pupils recognized by several linear and nonlinear parameters. Good pupils could be discriminated from pupils with bad results in learning to 80 \%. The results support the hypothesis mentioned above. One possible explanation for the poor regulation of balance in bad learners could be a deficit in the neural maturity. In future, further developments will be targeted on higher discrimination levels, possibly in order to predict school success. On the other hand, the effects of special movement exercises on the neural development in childhood will be the focus in our further work}, language = {en} } @article{ZaksPikovskijKurths1999, author = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {On the generalized dimensions for the fourier spectrum of the thue-morse sequence}, year = {1999}, 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} } @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{AgarwalMarwanMaheswaranetal.2020, author = {Agarwal, Ankit and Marwan, Norbert and Maheswaran, Rathinasamy and {\"O}zt{\"u}rk, Ugur and Kurths, J{\"u}rgen and Merz, Bruno}, title = {Optimal design of hydrometric station networks based on complex network analysis}, series = {Hydrology and Earth System Sciences}, volume = {24}, journal = {Hydrology and Earth System Sciences}, number = {5}, publisher = {Copernicus Publ.}, address = {G{\"o}ttingen}, issn = {1027-5606}, doi = {10.5194/hess-24-2235-2020}, pages = {2235 -- 2251}, year = {2020}, abstract = {Hydrometric networks play a vital role in providing information for decision-making in water resource management. They should be set up optimally to provide as much information as possible that is as accurate as possible and, at the same time, be cost-effective. Although the design of hydrometric networks is a well-identified problem in hydrometeorology and has received considerable attention, there is still scope for further advancement. In this study, we use complex network analysis, defined as a collection of nodes interconnected by links, to propose a new measure that identifies critical nodes of station networks. The approach can support the design and redesign of hydrometric station networks. The science of complex networks is a relatively young field and has gained significant momentum over the last few years in different areas such as brain networks, social networks, technological networks, or climate networks. The identification of influential nodes in complex networks is an important field of research. We propose a new node-ranking measure - the weighted degree-betweenness (WDB) measure - to evaluate the importance of nodes in a network. It is compared to previously proposed measures used on synthetic sample networks and then applied to a real-world rain gauge network comprising 1229 stations across Germany to demonstrate its applicability. The proposed measure is evaluated using the decline rate of the network efficiency and the kriging error. The results suggest that WDB effectively quantifies the importance of rain gauges, although the benefits of the method need to be investigated in more detail.}, language = {en} } @misc{AgarwalMarwanMaheswaranetal.2020, author = {Agarwal, Ankit and Marwan, Norbert and Maheswaran, Rathinasamy and {\"O}zt{\"u}rk, Ugur and Kurths, J{\"u}rgen and Merz, Bruno}, title = {Optimal design of hydrometric station networks based on complex network analysis}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {951}, issn = {1866-8372}, doi = {10.25932/publishup-47100}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471006}, pages = {19}, year = {2020}, abstract = {Hydrometric networks play a vital role in providing information for decision-making in water resource management. They should be set up optimally to provide as much information as possible that is as accurate as possible and, at the same time, be cost-effective. Although the design of hydrometric networks is a well-identified problem in hydrometeorology and has received considerable attention, there is still scope for further advancement. In this study, we use complex network analysis, defined as a collection of nodes interconnected by links, to propose a new measure that identifies critical nodes of station networks. The approach can support the design and redesign of hydrometric station networks. The science of complex networks is a relatively young field and has gained significant momentum over the last few years in different areas such as brain networks, social networks, technological networks, or climate networks. The identification of influential nodes in complex networks is an important field of research. We propose a new node-ranking measure - the weighted degree-betweenness (WDB) measure - to evaluate the importance of nodes in a network. It is compared to previously proposed measures used on synthetic sample networks and then applied to a real-world rain gauge network comprising 1229 stations across Germany to demonstrate its applicability. The proposed measure is evaluated using the decline rate of the network efficiency and the kriging error. The results suggest that WDB effectively quantifies the importance of rain gauges, although the benefits of the method need to be investigated in more detail.}, language = {en} } @article{ZaikinKurths2006, author = {Zaikin, Alexey and Kurths, J{\"u}rgen}, title = {Optimal length transportation hypothesis to model proteasome product size distribution}, series = {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}, volume = {32}, journal = {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}, number = {3-4}, publisher = {Springer}, address = {Dordrecht}, issn = {0092-0606}, doi = {10.1007/s10867-006-9014-z}, pages = {231 -- 243}, year = {2006}, abstract = {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.}, 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} } @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{MoshelZivotofskyLiangetal.2008, author = {Moshel, Shay and Zivotofsky, Ari Z. and Liang, Jin-Rong and Engbert, Ralf and Kurths, J{\"u}rgen and Kliegl, Reinhold and Havlin, Shlomo}, title = {Persistence and phase synchronization properties of fixational eye movement}, issn = {1951-6355}, year = {2008}, abstract = {When we fixate our gaze on a stable object, our eyes move continuously with extremely small involuntary and autonomic movements, that even we are unaware of during their occurrence. One of the roles of these fixational eye movements is to prevent the adaptation of the visual system to continuous illumination and inhibit fading of the image. These random, small movements are restricted at long time scales so as to keep the target at the centre of the field of view. In addition, the synchronisation properties between both eyes are related to binocular coordination in order to provide stereopsis. We investigated the roles of different time scale behaviours, especially how they are expressed in the different spatial directions (vertical versus horizontal). We also tested the synchronisation between both eyes. Results show different scaling behaviour between horizontal and vertical movements. When the small ballistic movements, i.e., microsaccades, are removed, the scaling behaviour in both axes becomes similar. Our findings suggest that microsaccades enhance the persistence at short time scales mostly in the horizontal component and much less in the vertical component. We also applied the phase synchronisation decay method to study the synchronisation between six combinations of binocular fixational eye movement components. We found that the vertical-vertical components of right and left eyes are significantly more synchronised than the horizontal-horizontal components. These differences may be due to the need for continuously moving the eyes in the horizontal plane in order to match the stereoscopic image for different viewing distances.}, language = {en} } @article{PikovskijRosenblumOsipovetal.1997, author = {Pikovskij, Arkadij and Rosenblum, Michael and Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Phase synchronization effects in a lattice of nonidentical R{\"o}ssler oscillators}, year = {1997}, language = {en} } @article{RosenblumPikovskijKurths1997, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase synchronization in driven and coupled chaotic oscillators}, year = {1997}, language = {en} } @article{IvanchenkoOsipovShalfeevetal.2004, author = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen}, title = {Phase synchronization in ensembles of bursting oscillators}, issn = {0031-9007}, year = {2004}, abstract = {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}, language = {en} } @article{RosenblumPikovskijKurths1997, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase synchronization in noisy and chaotic oscillators}, year = {1997}, language = {en} } @article{PikovskijRosenblumKurths2000, author = {Pikovskij, Arkadij and Rosenblum, Michael and Kurths, J{\"u}rgen}, title = {Phase synchronization in regular and chaotic systems}, issn = {0218-1274}, year = {2000}, language = {en} } @article{ParkZaksKurths1999, author = {Park, Eun Hyoung and Zaks, Michael A. and Kurths, J{\"u}rgen}, title = {Phase synchronization in the forced lorenz system}, year = {1999}, language = {en} } @article{IvanchenkoOsipovShalfeevetal.2004, author = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic intermittent oscillations}, issn = {0031-9007}, year = {2004}, abstract = {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}, language = {en} } @article{ZaksRosenblumPikovskijetal.1997, author = {Zaks, Michael A. and Rosenblum, Michael and Pikovskij, Arkadij and Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic oscillations in terms of periodic orbits}, issn = {1054-1500}, year = {1997}, language = {en} } @article{RosenblumOsipovPikovskijetal.1997, author = {Rosenblum, Michael and Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic oscillators by external driving}, year = {1997}, language = {en} } @article{OsipovPikovskijKurths2002, author = {Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase Synchronization of Chaotic Rotators}, year = {2002}, abstract = {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.}, language = {en} } @article{PikovskijRosenblumZaksetal.1999, author = {Pikovskij, Arkadij and Rosenblum, Michael and Zaks, Michael A. and Kurths, J{\"u}rgen}, title = {Phase synchronization of regular and chaotic oscillators}, year = {1999}, 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} } @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{WesselKonvickaWeidermannetal.2004, author = {Wessel, Niels and Konvicka, Jan and Weidermann, Frank and Nestmann, S. and Neugebauer, R. and Schwarz, U. and Wessel, A. and Kurths, J{\"u}rgen}, title = {Predicting thermal displacements in modular tool systems}, issn = {1054-1500}, year = {2004}, abstract = {In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally inducedaccuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems. errors can be estimated with 1-2 micrometer}, language = {en} } @article{BoersBarbosaBookhagenetal.2015, author = {Boers, Niklas and Barbosa, Henrique M. J. and Bookhagen, Bodo and Marengo, Jose A. and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Propagation of Strong Rainfall Events from Southeastern South America to the Central Andes}, series = {Journal of climate}, volume = {28}, journal = {Journal of climate}, number = {19}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0894-8755}, doi = {10.1175/JCLI-D-15-0137.1}, pages = {7641 -- 7658}, year = {2015}, abstract = {Based on high-spatiotemporal-resolution data, the authors perform a climatological study of strong rainfall events propagating from southeastern South America to the eastern slopes of the central Andes during the monsoon season. These events account for up to 70\% of total seasonal rainfall in these areas. They are of societal relevance because of associated natural hazards in the form of floods and landslides, and they form an intriguing climatic phenomenon, because they propagate against the direction of the low-level moisture flow from the tropics. The responsible synoptic mechanism is analyzed using suitable composites of the relevant atmospheric variables with high temporal resolution. The results suggest that the low-level inflow from the tropics, while important for maintaining sufficient moisture in the area of rainfall, does not initiate the formation of rainfall clusters. Instead, alternating low and high pressure anomalies in midlatitudes, which are associated with an eastward-moving Rossby wave train, in combination with the northwestern Argentinean low, create favorable pressure and wind conditions for frontogenesis and subsequent precipitation events propagating from southeastern South America toward the Bolivian Andes.}, language = {en} } @article{SaparinThomsenProhaskaetal.2005, author = {Saparin, P. I. and Thomsen, J. S. and Prohaska, Steffen and Zaikin, Alexei and Kurths, J{\"u}rgen and Hege, H. C. and Gowin, W.}, title = {Quantification of spatial structure of human proximal tibial bone biopsies using 3D measures of complexity}, issn = {0094-5765}, year = {2005}, abstract = {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}, language = {en} } @article{MarwanBellerFelsenbergetal.2012, author = {Marwan, Norbert and Beller, Gise and Felsenberg, Dieter and Saparin, Peter and Kurths, J{\"u}rgen}, title = {quantifying changes in the spatial structure of trabecular bone}, series = {International journal of bifurcation and chaos : in applied sciences and engineering}, volume = {22}, journal = {International journal of bifurcation and chaos : in applied sciences and engineering}, number = {2}, publisher = {World Scientific}, address = {Singapore}, issn = {0218-1274}, doi = {10.1142/S0218127412500277}, pages = {12}, year = {2012}, abstract = {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.}, language = {en} } @article{AgarwalMarwanMaheswaranetal.2018, author = {Agarwal, Ankit and Marwan, Norbert and Maheswaran, Rathinasamy and Merz, Bruno and Kurths, J{\"u}rgen}, title = {Quantifying the roles of single stations within homogeneous regions using complex network analysis}, series = {Journal of hydrology}, volume = {563}, journal = {Journal of hydrology}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0022-1694}, doi = {10.1016/j.jhydrol.2018.06.050}, pages = {802 -- 810}, year = {2018}, abstract = {Regionalization and pooling stations to form homogeneous regions or communities are essential for reliable parameter transfer, prediction in ungauged basins, and estimation of missing information. Over the years, several clustering methods have been proposed for regional analysis. Most of these methods are able to quantify the study region in terms of homogeneity but fail to provide microscopic information about the interaction between communities, as well as about each station within the communities. We propose a complex network-based approach to extract this valuable information and demonstrate the potential of our approach using a rainfall network constructed from the Indian gridded daily precipitation data. The communities were identified using the network-theoretical community detection algorithm for maximizing the modularity. Further, the grid points (nodes) were classified into universal roles according to their pattern of within- and between-community connections. The method thus yields zoomed-in details of individual rainfall grids within each community.}, language = {en} } @article{ShabuninAstakhovKurths2005, author = {Shabunin, A. and Astakhov, Vladimir V. and Kurths, J{\"u}rgen}, title = {Quantitative analysis of chaotic synchronization by means of coherence}, issn = {1539-3755}, year = {2005}, abstract = {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}, 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} } @article{RusconiVallerianiDunlopetal.2012, author = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard}, title = {Quantitative approach to the stochastics of bone remodeling}, series = {epl : a letters journal exploring the frontiers of physics}, volume = {97}, journal = {epl : a letters journal exploring the frontiers of physics}, number = {2}, publisher = {EDP Sciences}, address = {Mulhouse}, issn = {0295-5075}, doi = {10.1209/0295-5075/97/28009}, pages = {6}, year = {2012}, abstract = {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.}, 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{BaptistaBohnKliegletal.2008, author = {Baptista, Murilo da Silva and Bohn, Christiane and Kliegl, Reinhold and Engbert, Ralf and Kurths, J{\"u}rgen}, title = {Reconstruction of eye movements during blinks}, issn = {1054-1500}, doi = {10.1063/1.2890843}, year = {2008}, 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{VossKurthsSchwarz1996, author = {Voss, Henning U. and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Reconstruction of grand minima of solar activity from radiocarbon data : linear and nonlinear signal analysis}, year = {1996}, abstract = {Using a special technique of data analysis, we have found out 34 grand minima of solar activity in a 7,700 years long C14 record. The method used rests on a proper filtering of the C14 record and the extrapolation of verifiable results for the later history back in time. Additionally, we have applied a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of grand minima by Eddy, but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested esp. the model of Barnes et al. There are hints for that the grand minima might solely be driven by the 209--year period found in the C14 record.}, language = {en} } @book{VossKurthsSchwarz1996, author = {Voss, Henning U. and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Reconstruction of grand minima of solar activity from radiocarbon data : linear and nonlinear signal analysis}, series = {Preprint NLD}, volume = {28}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {14 S.}, year = {1996}, language = {en} } @article{VossKurths1997, author = {Voss, Henning U. and Kurths, J{\"u}rgen}, title = {Reconstruction of nonlinear time delay models from data by the use of optimal transformations}, year = {1997}, language = {en} } @article{VossKurths1999, author = {Voss, Henning U. and Kurths, J{\"u}rgen}, title = {Reconstruction of nonlinear time-delayed feedback models from optical data}, year = {1999}, language = {en} } @article{RamosBuilesJaramilloPovedaetal.2017, author = {Ramos, Antonio M. T. and Builes-Jaramillo, Alejandro and Poveda, German and Goswami, Bedartha and Macau, Elbert E. N. and Kurths, J{\"u}rgen and Marwan, Norbert}, title = {Recurrence measure of conditional dependence and applications}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {95}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.95.052206}, pages = {8}, year = {2017}, abstract = {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.}, language = {en} } @article{MarwanSchinkelKurths2013, author = {Marwan, Norbert and Schinkel, Stefan and Kurths, J{\"u}rgen}, title = {Recurrence plots 25 years later -Gaining confidence in dynamical transitions}, series = {epl : a letters journal exploring the frontiers of physics}, volume = {101}, journal = {epl : a letters journal exploring the frontiers of physics}, number = {2}, publisher = {EDP Sciences}, address = {Mulhouse}, issn = {0295-5075}, doi = {10.1209/0295-5075/101/20007}, pages = {6}, year = {2013}, abstract = {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.}, language = {en} } @article{WesselMarwanMeyerfeldtetal.2001, author = {Wessel, Niels and Marwan, Norbert and Meyerfeldt, Udo and Schirdewan, Alexander and Kurths, J{\"u}rgen}, title = {Recurrence quantification analysis to characterise the heart rate variability before the onset of ventricular tachycardia}, year = {2001}, abstract = {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}, language = {en} } @article{MarwanWesselMeyerfeldtetal.2002, author = {Marwan, Norbert and Wessel, Niels and Meyerfeldt, Udo and Schirdewan, Alexander and Kurths, J{\"u}rgen}, title = {Recurrence-plot-based measures of complexity and its application to heart-rate-variability data}, year = {2002}, abstract = {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.}, language = {en} } @article{OsipovKurths2002, author = {Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Regular and chaotic phase synchronization of coupled circle maps}, year = {2002}, language = {en} } @article{BergnerFrascaSciutoetal.2012, author = {Bergner, Andre and Frasca, M. and Sciuto, G. and Buscarino, A. and Ngamga, Eulalie Joelle and Fortuna, L. and Kurths, J{\"u}rgen}, title = {Remote synchronization in star networks}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {85}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.85.026208}, pages = {7}, year = {2012}, abstract = {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.}, 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{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{WuLiChenetal.2009, author = {Wu, Ye and Li, Ping and Chen, Maoyin and Xiao, Jinghua and Kurths, J{\"u}rgen}, title = {Response of scale-free networks with community structure to external stimuli}, issn = {0378-4371}, doi = {10.1016/j.physa.2009.03.037}, year = {2009}, abstract = {The response of scale-free networks with community structure to external stimuli is studied. By disturbing some nodes with different strategies, it is shown that the robustness of this kind of network can be enhanced due to the existence of communities in the networks. Some of the response patterns are found to coincide with topological communities. We show that such phenomena also occur in the cat brain network which is an example of a scale-free like network with community structure. Our results provide insights into the relationship between network topology and the functional organization in complex networks from another viewpoint.}, language = {en} } @article{LandaUshakovKurths2006, author = {Landa, Polina S. and Ushakov, Vladimir and Kurths, J{\"u}rgen}, title = {Rigorous theory of stochastic resonance in overdamped bistable oscillators for weak signals}, series = {Chaos, solitons \& fractals : applications in science and engineering}, volume = {30}, journal = {Chaos, solitons \& fractals : applications in science and engineering}, number = {3}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0960-0779}, doi = {10.1016/j.chaos.2005.08.116}, pages = {574 -- 578}, year = {2006}, abstract = {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.}, language = {en} }