@article{BaptistaKurths2005, author = {Baptista, Murilo da Silva and Kurths, J{\"u}rgen}, title = {Chaotic channel}, issn = {1539-3755}, year = {2005}, abstract = {This work combines the theory of chaotic synchronization with the theory of information in order to introduce the chaotic channel, an active medium formed by connected chaotic systems. This subset of a large chaotic net represents the path along which information flows. We show that the possible amount of information exchange between the transmitter, where information enters the net, and the receiver, the destination of the information, is proportional to the level of synchronization between these two special subsystems}, language = {en} } @article{FeudelWittGellertetal.2005, author = {Feudel, Fred and Witt, Annette and Gellert, Marcus and Kurths, J{\"u}rgen and Grebogi, Celso and Sanjuan, Miguel Angel Fernandez}, title = {Intersections of stable and unstable manifolds : the skeleton of Lagrangian chaos}, year = {2005}, abstract = {We study Hamiltonian chaos generated by the dynamics of passive tracers moving in a two-dimensional fluid flow and describe the complex structure formed in a chaotic layer that separates a vortex region from the shear flow. The stable and unstable manifolds of unstable periodic orbits are computed. It is shown that their intersections in the Poincare map as an invariant set of homoclinic points constitute the backbone of the chaotic layer. Special attention is paid to the finite time properties of the chaotic layer. In particular, finite time Lyapunov exponents are computed and a scaling law of the variance of their distribution is derived. Additionally, the box counting dimension as an effective dimension to characterize the fractal properties of the layer is estimated for different duration times of simulation. Its behavior in the asymptotic time limit is discussed. By computing the Lyapunov exponents and by applying methods of symbolic dynamics, the formation of the layer as a function of the external forcing strength, which in turn represents the perturbation of the originally integrable system, is characterized. In particular, it is shown that the capture of KAM tori by the layer has a remarkable influence on the averaged Lyapunov exponents. (C) 2004 Elsevier Ltd. All rights reserved}, language = {en} } @article{MotterZhouKurths2005, author = {Motter, Adilson E. and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Enhancing complex-network synchronization}, issn = {0295-5075}, year = {2005}, abstract = {Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for enhanced synchronization in weighted networks with asymmetric coupling. We show that, in the optimum regime, synchronizability is solely determined by the average degree and does not depend on the system size and the details of the degree distribution. In scale-free networks, where the average degree may increase with heterogeneity, synchronizability is drastically enhanced and may become positively correlated with heterogeneity, while the overall cost involved in the network coupling is significantly reduced as compared to the case of unwcighted coupling}, language = {en} } @article{VolkovUllnerKurths2005, author = {Volkov, E. I. and Ullner, Ekkehard and Kurths, J{\"u}rgen}, title = {Stochastic multiresonance in the coupled relaxation oscillators}, issn = {1054-1500}, year = {2005}, abstract = {We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh- Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency. (C) 2005 American Institute of Physics}, 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{MaraunKurths2005, author = {Maraun, Douglas and Kurths, J{\"u}rgen}, title = {Epochs of phase coherence between El Nino/Southern Oscillation and Indian monsoon}, issn = {0094-8276}, year = {2005}, abstract = {We present a modern method used in nonlinear time series analysis to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. We study the difference of the phase dynamics between El Nino/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales. We identify distinct epochs, especially two intervals of phase coherence, 1886 - 1908 and 1964 - 1980, corroborating earlier findings from a new point of view. A significance test shows that the coherence is very unlikely to be the result of stochastic fluctuations. We also detect so far unknown periods of coupling which are invisible to linear methods. These findings suggest that the decreasing correlation during the last decades might be a typical epoch of the ENSO/ Monsoon system having occurred repeatedly. The high time resolution of the method enables us to present an interpretation of how volcanic radiative forcing could cause the coupling}, 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{VianaGrebogiPintoetal.2005, author = {Viana, R. L. and Grebogi, Celso and Pinto, S. E. D. and Lopes, S. R. and Batista, A. M. and Kurths, J{\"u}rgen}, title = {Bubbling bifurcation : loss of synchronization and shadowing breakdown in complex systems}, year = {2005}, abstract = {Complex dynamical systems with many degrees of freedom may exhibit a wealth of collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of coupled logistic maps to investigate the relationship between the loss of chaos synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization manifold. This has been confirmed by numerical diagnostics of synchronization and non-hyperbolic behavior, the latter using the statistical properties of finite-time Lyapunov exponents. (c) 2005 Elsevier B.V. All rights reserved}, 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{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{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} } @article{MontbrioKurthsBlasius2004, author = {Montbrio, Ernest and Kurths, J{\"u}rgen and Blasius, Bernd}, title = {Synchronization of two interacting populations of oscillators}, year = {2004}, abstract = {We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed.}, language = {en} } @article{AllefeldKurths2004, author = {Allefeld, Carsten and Kurths, J{\"u}rgen}, title = {An approach to multivariate phase synchronization analysis and its application to event-related potentials}, issn = {0218-1274}, year = {2004}, abstract = {A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields}, language = {en} } @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{AnishchenkoVadivasovaKurthsetal.2004, author = {Anishchenko, Vadim S. and Vadivasova, T. E. and Kurths, J{\"u}rgen and Okrokvertskhov, G. A. and Strelkova, G. I.}, title = {Autocorrelation function and spectral linewidth of spiral chaos in a physical experiment}, issn = {1063-651X}, year = {2004}, abstract = {We present results of physical experiments where we measure the autocorrelation function (ACF) and the spectral linewidth of the basic frequency of a spiral chaotic attractor in a generator with inertial nonlinearity both without and in the presence of external noise. It is shown that the ACF of spiral attractors decays according to an exponential law with a decrement which is defined by the phase diffusion coefficient. It is also established that the evolution of the instantaneous phase can be approximated by a Wiener random process}, language = {en} } @article{BeimGrabenSaddyKurths2004, author = {Beim Graben, Peter and Saddy, Douglas and Kurths, J{\"u}rgen}, title = {Untitled}, year = {2004}, language = {de} } @article{LindTitzKuhlbrodtetal.2004, author = {Lind, P. G. and Titz, Sven Holger and Kuhlbrodt, Till and Corte-Real, J. A. M. and Kurths, J{\"u}rgen and Gallas, J. A. C. and Feudel, Ulla}, title = {Coupled bistable maps : a tool to study convection parameterization in ocean models}, issn = {0218-1274}, year = {2004}, abstract = {We present a study of ocean convection parameterization based on a novel approach which includes both eddy diffusion and advection and consists of a two-dimensional lattice of bistable maps. This approach retains important features of usual grid models and allows to assess the relative roles of diffusion and advection in the spreading of convective cells. For large diffusion our model exhibits a phase transition from convective patterns to a homogeneous state over the entire lattice. In hysteresis experiments we find staircase behavior depending on stability thresholds of local convection patterns. This nonphysical behavior is suspected to induce spurious abrupt changes in the spreading of convection in ocean models. The final steady state of convective cells depends not only on the magnitude of the advective velocity but also on its direction, implying a possible bias in the development of convective patterns. Such bias points to the need for an appropriate choice of grid geometry in ocean modeling}, language = {en} } @article{AllefeldKurths2004, author = {Allefeld, Carsten and Kurths, J{\"u}rgen}, title = {Testing for phase synchronization}, issn = {0218-1274}, year = {2004}, abstract = {We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series}, language = {en} } @article{GamezZhouTimmermannetal.2004, author = {Gamez, A. J. and Zhou, Changsong and Timmermann, A. and Kurths, J{\"u}rgen}, title = {Nonlinear dimensionality reduction in climate data}, issn = {1023-5809}, year = {2004}, abstract = {Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence that makes the selection of a proper minimum number of subspaces for successfully representing the variability of the process ambiguous. The use of nonlinear methods can improve the embedding of multivariate data into lower dimensional manifolds. In this article, a nonlinear method for dimensionality reduction, Isomap, is applied to the sea surface temperature and thermocline data in the tropical Pacific Ocean, where the El Nino-Southern Oscillation (ENSO) phenomenon and the annual cycle phenomena interact. Isomap gives a more accurate description of the manifold dimensionality of the physical system. The knowledge of the minimum number of dimensions is expected to improve the development of low dimensional models for understanding and predicting ENSO}, language = {en} } @article{BoveBoccalettiBragardetal.2004, author = {Bove, I. and Boccaletti, Stefano and Bragard, Jean and Kurths, J{\"u}rgen and Mancini, H.}, title = {Frequency entrainment of nonautonomous chaotic oscillators}, year = {2004}, abstract = {We give evidence of frequency entrainment of dominant peaks in the chaotic spectra of two coupled chaotic nonautonomous oscillators. At variance with the autonomous case, the phenomenon is here characterized by the vanishing of a previously positive Lyapunov exponent in the spectrum, which takes place for a broad range of the coupling strength parameter. Such a state is studied also for the case of chaotic oscillators with ill-defined phases due to the absence of a unique center of rotation. Different phase synchronization indicators are used to circumvent this difficulty}, language = {en} } @article{MaraunKurths2004, author = {Maraun, Douglas and Kurths, J{\"u}rgen}, title = {Cross wavelet analysis: significance testing and pitfalls}, issn = {1023-5809}, year = {2004}, abstract = {In this paper, we present a detailed evaluation of cross wavelet analysis of bivariate time series. We develop a statistical test for zero wavelet coherency based on Monte Carlo simulations. If at least one of the two processes considered is Gaussian white noise, an approximative formula for the critical value can be utilized. In a second part, typical pitfalls of wavelet cross spectra and wavelet coherency are discussed. The wavelet cross spectrum appears to be not suitable for significance testing the interrelation between two processes. Instead, one should rather apply wavelet coherency. Furthermore we investigate problems due to multiple testing. Based on these results, we show that coherency between ENSO and NAO is an artefact for most of the time from 1900 to 1995. However, during a distinct period from around 1920 to 1940, significant coherency between the two phenomena occurs}, language = {en} } @article{RomanoThielKurthsetal.2004, author = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and von Bloh, Werner}, title = {Multivariate recurrence plots}, issn = {0375-9601}, year = {2004}, abstract = {We propose a new approach to calculate recurrence plots of multivariate time series, based on joint recurrences in phase space. This new method allows to estimate dynamical invariants of the whole system, like the joint Renyi entropy of second order. We use this entropy measure to quantitatively study in detail the phase synchronization of two bidirectionally coupled chaotic systems and identify different types of transitions to chaotic phase synchronization in dependence on the coupling strength and the frequency mismatch. By means of this analysis we find several new phenomena, such a chaos-period-chaos transition to phase synchronization for rather large coupling strengths. (C) 2004 Elsevier B.V. All rights reserved}, language = {en} } @article{ThielRomanoSchwarzetal.2004, author = {Thiel, M. and Romano, Maria Carmen and Schwarz, Udo and Kurths, J{\"u}rgen and Timmer, Jens}, title = {Surrogate-based hypothesis test without surrogates}, issn = {0218-1274}, year = {2004}, abstract = {Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1}, language = {en} } @article{VossTimmerKurths2004, author = {Voss, Henning U. and Timmer, Jens and Kurths, J{\"u}rgen}, title = {Nonlinear dynamical system identification from uncertain and indirect measurements}, issn = {0218-1274}, year = {2004}, abstract = {We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples}, language = {en} } @article{ZhouKurths2004, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Resonant patterns in noisy active media}, issn = {1063-651X}, year = {2004}, abstract = {We investigate noise-controlled resonant response of active media to weak periodic forcing, both in excitable and oscillatory regimes. In the excitable regime, we find that noise-induced irregular wave structures can be reorganized into frequency-locked resonant patterns by weak signals with suitable frequencies. The resonance occurs due to a matching condition between the signal frequency and the noise-induced inherent time scale of the media. m:1 resonant regions similar to the Arnold tongues in frequency locking of self-sustained oscillatory media are observed. In the self-sustained oscillatory regime, noise also controls the oscillation frequency and reshapes significantly the Arnold tongues. The combination of noise and weak signal thus could provide an efficient tool to manipulate active extended systems in experiments}, language = {en} } @article{TokudaKurthsAllariaetal.2004, author = {Tokuda, I. and Kurths, J{\"u}rgen and Allaria, Eugenio and Meucci, Riccardo and Boccaletti, Stefano and Arecchi, Fortunato Tito}, title = {Predicting phase synchronization in a spiking chaotic CO2 laser}, issn = {1063-651X}, year = {2004}, abstract = {An approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2 laser from experimental data. We analyze this laser system in a regime able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as nonsynchronization in a broad parameter space of forcing frequency and amplitude without further experiments}, language = {en} } @article{ThielRomanoKurths2004, author = {Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen}, title = {How much information is contained in a recurrence plot?}, issn = {0375-9601}, year = {2004}, abstract = {Recurrence plots have recently been recognized as a powerful tool for the analysis of data. Not only the visualization of structures of the time series but also the possibility to estimate invariants from them and the possibility to analyze non-stationary data sets are remarkable. However, the question of how much information is encoded in such a two-dimensional and binary representation has not been discussed so far. In this Letter we show that-under some conditions-it is possible to reconstruct an attractor from the recurrence plot, at least topologically. This means that all relevant dynamical information is contained in the plot. (C) 2004 Elsevier B.V. All rights reserved}, language = {en} } @article{ThielRomanoReadetal.2004, author = {Thiel, M. and Romano, Maria Carmen and Read, P. L. and Kurths, J{\"u}rgen}, title = {Estimation of dynamical invariants without embedding by recurrence plots}, issn = {1054-1500}, year = {2004}, abstract = {In this paper we show that two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay. This fact is interesting as these quantities are even invariant if no embedding is used. This is an important advantage of RPs compared to other techniques of nonlinear data analysis. These estimates for the correlation dimension and entropy are robust and, moreover, can be obtained at a low numerical cost. We exemplify our results for the Rossler system, the funnel attractor and the Mackey-Glass system. In the last part of the paper we estimate dynamical invariants for data from some fluid dynamical experiments and confirm previous evidence for low dimensional chaos in this experimental system. (C) 2004 American Institute of Physics}, language = {en} } @article{SpahnKrivovSremcevicetal.2003, author = {Spahn, Frank and Krivov, Alexander V. and Sremcevic, Miodrag and Schwarz, U. and Kurths, J{\"u}rgen}, title = {Stochastic forces in circumplanetary dust dynamics}, year = {2003}, abstract = {Charged dust grains in circumplanetary environments experience, beyond various deterministic forces, also stochastic perturbations caused, by fluctuations of the magnetic field, the charge of the grains, by chaotic rotation of aspherical grains, etc. Here we investigate the dynamics of a dust population in a circular orbit around a planet which is perturbed by a stochastic planetary magnetic field B', modeled by an isotropically Gaussian white noise. The resulting perturbation equations give rise to a modified diffusion of the inclinations i and eccentricities e. The diffusion coefficient is found to be D proportional to w^2 O /n^2 , where the gyrofrequency, the Kepler frequency, and the synodic frequency are denoted by w , O, and n, respectively. This behavior has been checked against numerical simulations. We have chosen dust grains (1 m in radius) ejected from Jupiter's satellite Europa in circular equatorial orbits around Jupiter and integrated numerically their trajectories over their typical lifetimes (100 years). The particles were exposed to a Gaussian fluctuating magnetic field B' with the same statistical properties as in the analytical treatment. These simulations have confirmed the analytical results. The theoretical studies showed the statistical properties of B' to be of decisive importance. To estimate them, we analyzed the magnetic field data obtained by the Galileo spacecraft magnetometer at Jupiter and found almost Gaussian fluctuations of about 5\% of the mean field and exponentially decaying correlations. This results in a diffusion of orbital inclinations and eccentricities of the dust grains of about ten percent over the lifetime of the particles. For smaller dusty motes or for close-in particles (e.g., in Jovian gossamer rings) stochastics might well dominate the dynamics.}, language = {en} } @article{AnishchenkoVadivasovaKopeikinetal.2003, author = {Anishchenko, Vadim S. and Vadivasova, T. E. and Kopeikin, A. S. and Strelkova, G. I. and Kurths, J{\"u}rgen}, title = {Spectral and correlation analysis of spiral chaos}, issn = {0219-4775}, year = {2003}, abstract = {We study numerically the behavior of the autocorrelation function (ACF) and the power spectrum of spiral attractors without and in the presence of noise. It is shown that the ACF decays exponentially and has two different time scales. The rate of the ACF decrease is defined by the amplitude fluctuations on small time intervals, i.e., when tau < tau(cor), and by the effective diffusion coefficient of the instantantaneous phase on large time intervals. it is also demonstrated that the ACF in the Poincare map also decreases according to the exponential law exp(-lambda(+)k), where lambda(+) is the positive Lyapunov exponent. The obtained results are compared with the theory of fluctuations for the Van der Pol oscillator}, language = {en} } @article{PetrovKurthsGeorgiev2003, author = {Petrov, Valko and Kurths, J{\"u}rgen and Georgiev, Nikola}, title = {Reconstructing differential equation from a time series}, issn = {0218-1274}, year = {2003}, abstract = {This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient}, language = {en} } @article{SteuerZhouKurths2003, author = {Steuer, Ralf and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Constructive effects of fluctuations in genetic and biochemical regulatory systems}, issn = {0303-2647}, year = {2003}, abstract = {Biochemical and genetic regulatory systems that involve low concentrations of molecules are inherently noisy. This intrinsic stochasticity, has received considerable interest recently, leading to new insights about the sources and consequences of noise in complex systems of genetic regulation. However, most prior work was devoted to the reduction of fluctuation and the robustness of cellular function with respect to intrinsic noise. Here, we focus on several scenarios in which the inherent molecular fluctuations are not merely a nuisance, but act constructively and bring about qualitative changes in the dynamics of the system. It will be demonstrated that in many typical situations biochemical and genetic regulatory systems may utilize intrinsic noise to their advantage. (C) 2002 Elsevier Ireland Ltd. All rights reserved}, language = {en} } @article{SteuerKurthsFiehnetal.2003, author = {Steuer, Ralf and Kurths, J{\"u}rgen and Fiehn, Oliver and Weckwerth, Wolfram}, title = {Interpreting correlations in metabolomic networks}, issn = {0300-5127}, year = {2003}, abstract = {Correlations, as observed between the concentrations of metabolites in a biological sample, may be used to gain additional information about the physiological state of a given tissue. in this mini-review, we discuss the integration of these observed correlations into metabolomic networks and their relationships with the underlying biochemical pathways}, language = {en} } @article{VianaGrebogiPintoetal.2003, author = {Viana, R. L. and Grebogi, Celso and Pinto, Seds and Lopes, S. R. and Batista, A. M. and Kurths, J{\"u}rgen}, title = {Validity of numerical trajectories in the synchronization transition of complex systems}, issn = {1063-651X}, year = {2003}, abstract = {We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties}, language = {en} } @article{VolkovUllnerZaikinetal.2003, author = {Volkov, E. I. and Ullner, Ekkehard and Zaikin, Alexei A. and Kurths, J{\"u}rgen}, title = {Frequency-dependent stochastic resonance in inhibitory coupled excitable systems}, issn = {1063-651X}, year = {2003}, abstract = {We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise- supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations}, language = {en} } @article{WesselSchwarzSaparinetal.2002, author = {Wessel, Niels and Schwarz, Udo and Saparin, Peter and Kurths, J{\"u}rgen}, title = {Symbolic dynamics for medical data analysis}, isbn = {3-936142-09-2}, year = {2002}, abstract = {Observational data of natural systems, as measured in medical measurements are typically quite different from those obtained in laboratories. Due to the peculiarities of these data, wellknown characteristics, such as power spectra or fractal dimension, often do not provide a suitable description. To study such data, we present here some measures of complexity, which are basing on symbolic dynamics. Firstly, a motivation for using symbolic dynamics and measures of complexity in data analysis based on the logistic map is given and next, two applications to medical data are shown. We demonstrate that symbolic dynamics is a useful tool for the risk assessment of patients after myocardial infarction as well as for the evaluation of th e architecture of human cancellous bone.}, language = {en} } @article{EbelingMolgedeyKurthsetal.2002, author = {Ebeling, Werner and Molgedey, Lutz and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Entropy, complexity, predictability, and data analysis of time series and letter sequences}, isbn = {3-540-41324-3}, year = {2002}, abstract = {The structure of time series and letter sequences is investigated using the concepts of entropy and complexity. First conditional entropy and transinformation are introduced and several generalizations are discussed. Further several measures of complexity are introduced and discussed. The capability of these concepts to describe the structure of time series and letter sequences generated by nonlinear maps, data series from meteorology, astrophysics, cardiology, cognitive psychology and finance is investigated. The relation between the complexity and the predictability of informational strings is discussed. The relation between local order and the predictability of time series is investigated.}, language = {en} } @article{BaltanasZaikinFeudeletal.2002, author = {Baltan{\´a}s, J. P. and Zaikin, Alexei A. and Feudel, Fred and Kurths, J{\"u}rgen and Sanjuan, Miguel Angel Fern{\´a}ndez}, title = {Noise-induced effects in tracer dynamics}, year = {2002}, language = {en} } @article{ZaikinGarciaOjalvoSchimanskyGeieretal.2002, author = {Zaikin, Alexei A. and Garc{\´i}a-Ojalvo, Jordi and Schimansky-Geier, Lutz and Kurths, J{\"u}rgen}, title = {Noise induced propagation in monostable media}, year = {2002}, abstract = {We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium i observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.}, language = {en} } @article{ZaikinLopezBaltanasetal.2002, author = {Zaikin, Alexei A. and L{\´o}pez, L and Baltan{\´a}s, J. P. and Kurths, J{\"u}rgen and Sanjuan, Miguel Angel Fern{\´a}ndez}, title = {Vibrational resonance in noise-induced structure}, year = {2002}, abstract = {We report on the effect of vibrational resonance in a spatially extended system of coupled noisy oscillators under the action of two periodic forces, a low-frequency one (signal) and a high-frequency one (carrier). Vibrational resonance manifests itself in the fact that for optimally selected values of high-frequency force amplitude, the response of the system to a low-frequency signal is optimal. This phenomenon is a synthesis of two effects, a noise- induced phase transition leading to bistability, and a conventional vibrational resonance, resulting in the optimization of signal processing. Numerical simulations, which demonstrate this effect for an extended system, can be understood by means of a zero-dimensional "effective" model. The behavior of this "effective" model is also confirmed by an experimental realization of an electronic circuit.}, language = {en} } @article{SitzSchwarzKurthsetal.2002, author = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen and Voss, Henning U.}, title = {Estimation of parameters and unobserved components for nonlinear systems from noisy time series}, year = {2002}, abstract = {We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data.}, language = {en} } @unpublished{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Characterizing the dynamics of stochastic bistable systems by measures of complexity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14556}, year = {1997}, abstract = {The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.}, language = {en} } @misc{KoseskaZaikinKurthsetal.2009, author = {Koseska, Aneta and Zaikin, Alexey and Kurths, J{\"u}rgen and Garc{\´i}a-Ojalvo, Jordi}, title = {Timing cellular decision making under noise via cell-cell communication}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-45260}, year = {2009}, abstract = {Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact.}, language = {en} } @unpublished{WittKurthsKrauseetal.1994, author = {Witt, Annette and Kurths, J{\"u}rgen and Krause, F. and Fischer, K.}, title = {On the validity of a model for the reversals of the Earth's magnetic field}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13460}, year = {1994}, abstract = {We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.}, language = {en} } @unpublished{KurthsVossWittetal.1994, author = {Kurths, J{\"u}rgen and Voss, A. and Witt, Annette and Saparin, P. and Kleiner, H. J. and Wessel, Niels}, title = {Quantitative analysis of heart rate variability}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13470}, year = {1994}, abstract = {In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.}, language = {en} } @unpublished{ThiessenhusenEspositoKurthsetal.1995, author = {Thiessenhusen, Kai-Uwe and Esposito, Larry W. and Kurths, J{\"u}rgen and Spahn, Frank}, title = {Detection of hidden resonances in Saturn's B-ring}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13618}, year = {1995}, abstract = {The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.}, language = {en} } @unpublished{VossKurthsSchwarz1996, author = {Voss, Henning and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14083}, year = {1996}, abstract = {Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.}, language = {en} } @article{ShuklaAgarwalSachdevaetal.2018, author = {Shukla, Roopam and Agarwal, Ankit and Sachdeva, Kamna and Kurths, J{\"u}rgen and Joshi, P. K.}, title = {Climate change perception}, series = {Climatic change : an interdisciplinary, intern. journal devoted to the description, causes and implications of climatic change}, volume = {152}, journal = {Climatic change : an interdisciplinary, intern. journal devoted to the description, causes and implications of climatic change}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {0165-0009}, doi = {10.1007/s10584-018-2314-z}, pages = {103 -- 119}, year = {2018}, abstract = {Climate change and variability have created widespread risks for farmers' food and livelihood security in the Himalayas. However, the extent of impacts experienced and perceived by farmers varies, as there is substantial diversity in the demographic, social, and economic conditions. Therefore, it is essential to understand how farmers with different resource-endowment and household characteristics perceive climatic risks. This study aims to analyze how farmer types perceive climate change processes and its impacts to gain insight into locally differentiated concerns by farming communities. The present study is based in the Uttarakhand state of Indian Western Himalayas. We examine farmer perceptions of climate change and how perceived impacts differ across farmer types. Primary household interviews with farming households (n = 241) were done in Chakrata and Bhikiyasian tehsil in Uttarakhand, India. In addition, annual and seasonal patterns of historical data of temperature (1951-2013) and precipitation (1901-2013) were analyzed to estimate trends and validate farmers' perception. Using statistical methods farmer typology was constructed, and five unique farmer types are identified. Majority of respondents across all farmer types noticed a decrease in summer and winter precipitation and an increase in summer temperature. Whereas the perceptions of impacts of climate change diverged across farmer types, as specific farmer types exclusively experienced few impacts. Impact of climatic risks on household food security and income was significantly perceived stronger by low-resource-endowed subsistence farmers, whereas the landless farmer type exclusively felt impacts on the communities social bond. This deeper understanding of the differentiated perception of impacts has strong implications for agricultural and development policymaking, highlighting the need for providing flexible adaptation options rather than specific solutions to avoid inequalities in fulfilling the needs of the heterogeneous farming communities.}, language = {en} } @article{PalusKurthsSchwarzetal.2007, author = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Seehafer, Norbert and Novotna, Dagmar and Charvatova, Ivanka}, title = {The solar activity cycle is weakly synchronized with the solar inertial motion}, doi = {10.1016/j.physleta.2007.01.039}, year = {2007}, abstract = {We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM.}, language = {en} } @article{KurthsSeehaferSpahn1999, author = {Kurths, J{\"u}rgen and Seehafer, Norbert and Spahn, Frank}, title = {Nichtlineare Dynamik in der Physik : Forschungsbeispiele und Forschungstrends}, isbn = {3-540-65329- 5}, year = {1999}, language = {de} } @misc{AllefeldKurths2004, author = {Allefeld, Carsten and Kurths, J{\"u}rgen}, title = {Testing for phase synchronization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20091}, year = {2004}, abstract = {We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-samples test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.}, language = {en} } @misc{AllefeldKurths2004, author = {Allefeld, Carsten and Kurths, J{\"u}rgen}, title = {An approach to multivariate phase synchronization analysis and its application to event-related potentials}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20106}, year = {2004}, abstract = {A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.}, language = {en} } @unpublished{GuastiEngbertKrampeetal.2000, author = {Guasti, Giovanna and Engbert, Ralf and Krampe, Ralf T. and Kurths, J{\"u}rgen}, title = {Phase transitions, complexity, and stationarity in the production of polyrhythms}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14933}, year = {2000}, abstract = {Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook}, language = {en} } @misc{LiMeiXuetal.2020, author = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf}, title = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {974}, issn = {1866-8372}, doi = {10.25932/publishup-47454}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-474542}, pages = {28}, year = {2020}, abstract = {This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the It{\^o} calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.}, language = {en} } @article{LiMeiXuetal.2020, author = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf}, title = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity}, series = {New Journal of Physics}, volume = {22}, journal = {New Journal of Physics}, publisher = {Dt. Physikalische Ges.}, address = {Bad Honnef}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab81b9}, pages = {27}, year = {2020}, abstract = {This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the It{\^o} calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.}, language = {en} } @article{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} } @article{ScheffczykEngbertKrampeetal.1996, author = {Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen and Rosenblum, Michael and Zaikin, Alexei A.}, title = {Nonlinear Modelling of Polyrhythmic Hand Movements}, year = {1996}, language = {en} } @article{KomalapriyaRomanoBlascoThieletal.2009, author = {Komalapriya, Chandrasekaran and Romano Blasco, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Simonotto, Jennifer and Furman, Michael and Ditto, William L. and Carney, Paul R.}, title = {Analysis of high-resulution microelectrode EEG recordings in an animal model of spontaneous limbic seizures}, issn = {0218-1274}, doi = {10.1142/S0218127409023226}, year = {2009}, language = {en} } @article{SureshSenthilkumarLakshmananetal.2010, author = {Suresh, R. and Senthilkumar, Dharmapuri Vijayan and Lakshmanan, Muthusamy and Kurths, J{\"u}rgen}, title = {Global phase synchronization in an array of time-delay systems}, issn = {1539-3755}, doi = {10.1103/Physreve.82.016215}, year = {2010}, abstract = {We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.}, language = {en} } @article{VincentKenfackSenthilkumaretal.2010, author = {Vincent, Uchechukwu E. and Kenfack, Anatole and Senthilkumar, Dharmapuri Vijayan and Mayer, Dieter and Kurths, J{\"u}rgen}, title = {Current reversals and synchronization in coupled ratchets}, issn = {1539-3755}, doi = {10.1103/Physreve.82.046208}, year = {2010}, abstract = {Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a current-reversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold k(th), a specific driving amplitude a(opt) is found for which the transport is optimum.}, language = {en} } @article{SchelterWinterhalderDahlhausetal.2006, author = {Schelter, Bj{\"o}rn and Winterhalder, Matthias and Dahlhaus, Rainer and Kurths, J{\"u}rgen and Timmer, Jens}, title = {Partial phase synchronization for multivariate synchronizing systems}, doi = {10.1103/Physrevlett.96.208103}, year = {2006}, abstract = {Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated}, language = {en} } @article{ZhouKurths2006, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Dynamical weights and enhanced synchronization in adaptive complex networks}, doi = {10.1103/Physrevlett.96.164102}, year = {2006}, abstract = {Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks}, language = {en} } @article{ZhouMotterKurths2006, author = {Zhou, Changsong and Motter, Adilson E. and Kurths, J{\"u}rgen}, title = {Universality in the synchronization of weighted random networks}, doi = {10.1103/Physrevlett.96.034101}, year = {2006}, abstract = {Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters}, language = {en} } @article{LiChenWuetal.2009, author = {Li, Ping and Chen, Maoyin and Wu, Ye and Kurths, J{\"u}rgen}, title = {Matrix-measure criterion for synchronization in coupled-map networks}, issn = {1539-3755}, doi = {10.1103/Physreve.79.067102}, year = {2009}, abstract = {We present conditions for the local and global synchronizations in coupled-map networks using the matrix measure approach. In contrast to many existing synchronization conditions, the proposed synchronization criteria do not depend on the solution of the synchronous state and give less limitation on the network connections. Numerical simulations of the coupled quadratic maps demonstrate the potentials of our main results.}, language = {en} } @article{KliemSchwarzKurthsetal.1998, author = {Kliem, Bernhard and Schwarz, Udo and Kurths, J{\"u}rgen and Dennis, Brian and Schwartz, Richard and Aschwanden, Markus J.}, title = {Wavelet analysis of solar flare hard X-ray}, issn = {0004-637x}, year = {1998}, language = {en} } @article{ZaikinRosenblumLandaetal.1998, author = {Zaikin, Alexei A. and Rosenblum, Michael and Landa, Polina S. and Kurths, J{\"u}rgen}, title = {On-off itermittency phenomena in a pendulum with a randomly vibrating suspension axis}, year = {1998}, language = {en} } @article{EngbertHainzlZoelleretal.1998, author = {Engbert, Ralf and Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen}, title = {Testing for unstable periodic orbits to characterize spatiotemporal dynamics}, year = {1998}, language = {en} } @article{SchwarzKurthsSpahnetal.1998, author = {Schwarz, Udo and Kurths, J{\"u}rgen and Spahn, Frank and Petzschmann, Olaf}, title = {Reply on the comment of "Clustering of granular assemblies with temperature dependent restitution and under differential rotation"}, year = {1998}, language = {en} } @article{KurthsKliemSchwarzetal.1998, author = {Kurths, J{\"u}rgen and Kliem, Bernhard and Schwarz, Udo and Kr{\"u}ger, Albrecht and Urpo, S.}, title = {Multiresolution analysis of solar mm-wave bursts}, year = {1998}, language = {en} } @article{KimKurthsKimetal.1998, author = {Kim, G. G. and Kurths, J{\"u}rgen and Kim, S. and Cao, L. Y.}, title = {Detecting determinism in human posture control data}, year = {1998}, language = {en} } @article{RosenblumKurthsSchaeferetal.1998, author = {Rosenblum, Michael and Kurths, J{\"u}rgen and Sch{\"a}fer, Carsten and Abel, Hans-Henning}, title = {Heartbeat synchronized with ventilation}, year = {1998}, language = {en} } @article{HnatkovaVesselVossetal.1998, author = {Hnatkova, Katarina and Vessel, N. and Voss, Andreas and Kurths, J{\"u}rgen and Sander, A. and Schirdewan, Alexander and Camm, A. J. and Malik, Marek}, title = {Multiparametric analysis of heart rate variability used for risk stratification among survivors of acute myocardial infarction}, issn = {0895-2795}, year = {1998}, language = {en} } @article{KurthsSchwarz1993, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Application of techniques of nonlinear dynamics to SS Cyg}, isbn = {0-7503-0282-8}, year = {1993}, abstract = {We look for structural properties in the light curve of the dwarf nova SS Cyg by means of techniques from nonlinear dynamics. Applying the popular Grassberger-Procaccia procedure, Cannizzo and Goddings (1988) showed that there is no evidence for a low-dimensional attractor underlying this record. Because there are some hints for order in the light curve, we search for other signatures of deterministic systems. Therefore, we use other methods recently developed in this theory, such as local linear prediction and recurrence maps. Our main findings are: i] the prediction error grows exponentially during outburst phases, but via a power law in the quiescent states, ii] there are some rather regular patterns in this light curve which sometimes recur, but the recurrence is not regular. This leads to the following conclusions: i] The outburst dynamics shows a higher degree of order than the quiescent one. There are some hints for deterministic chaos in the outburst behavior. ii] The light curve is a complex mixture of deterministic and stochastic structures. The analysis presented in this paper shows that methods of nonlinear dynamics can be an efficient tool for the study of complex processes, even if there is no evidence for a low-dimensional attractor.}, language = {en} } @article{SchwarzBenzKurthsetal.1993, author = {Schwarz, udo and Benz, Arnold O. and Kurths, J{\"u}rgen and Witt, Annette}, title = {Analysis of solar spike events by means of symbolic dynamics methods}, issn = {004-6361}, year = {1993}, abstract = {Using quantities of symbolic dynamics, such as mutual information, Shannon information and algorithmic complexity, we have searched for interrelations of spikes emitted simultaneously at different frequencies during the impulsive phase of a flare event. As the spikes are related to the flare energy release and are interpreted as emissions originating at different sites having different magnetic field strengths, any relation in frequency is interpretated as a relation in space. This approach is appropriate to characterize such spatio-temporal patterns, whereas the popular estimate of fractal dimensions can be applied to low-dimensional systems only. Depending on the energy release and emission processes, two types of fragmentation are possible: a scenario of global organization (spikes are emitted in a succession of similar events by the same system) or a scenario of local organization (many systems triggered by an initial event). Mutual information which is a generalization of correlation indicates a relation in frequency beyond the bandwidth of individual spikes. The scans in the spectrograms with large mutual information also show a low level of Shannon information and algorithmic complexity, indicating that the simultaneous appearance of spikes at other frequencies is not a completely stochastic phenomenon (white noise). It may be caused by a nonlinear deterministic system or by a Markov process. By means of mutual information we find a memory over frequency intervals up to 60 MHz. Shannon information and algorithmic complexity concern the mbox{whole} frequency region, i.e. the global source region. A global organization is also apparent in quasi-periodic changes of the Shannon information and algorithmic complexity in the range of 2 - 8 seconds. The finding is compatible with a scenario of local organization in which the information of one event spreads spatially and triggers further events at different places. The region is not an ensemble of independently flashing sources, each representing a system that cascades in energy after an initial trigger. On the contrary, there is a causal connection between the sources at any time. The analysis of the four spike events suggests that the structure in frequency is not stochastic but a process in which spikes at nearby locations are simultaneously triggered by a common exciter.}, language = {en} } @article{FlorenceDahlemAlmeidaetal.2009, author = {Florence, Gerson and Dahlem, Markus A. and Almeida, Ant{\^o}nio-Carlos G. and Bassani, Jos{\´e} W. M. and Kurths, J{\"u}rgen}, title = {The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression : a computational study}, issn = {0022-5193}, doi = {10.1016/j.jtbi.2009.01.032}, year = {2009}, abstract = {Experimental evidences point Out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular tons) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K+](o) and a decrease of extracellular calcium concentration [Ca2+](o) which raises the neuronal excitability. However, whether the high [K+](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K+](o) and zero [Ca2+](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na+-K+ pump, ion diffusion and glial buffering. Within these Conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na+- K+ pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K+ dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K+](o), transiting to an elevated state of neuronal excitability. Effects of high [K+](o), are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K+](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K+](o) by outward K+ flow depresses K+ Currents in a positive feedback way. At the last stage, due to the depression of K+ currents, the Na+-K+ pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K+](o) dynamics may play a fundamental role in these abnormal oscillatory patterns.}, 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} } @article{BaptistaZhouKurths2006, author = {Baptista, Murilo da Silva and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Information transmission in phase synchronous chaotic arrays}, issn = {0256-307X}, doi = {10.1088/0256-307X/23/3/010}, year = {2006}, abstract = {We show many versatile phase synchronous configurations that emerge in an array of coupled chaotic elements due to the presence of a periodic stimulus. Then, we explain the relevance of these configurations to the understanding of how information about such a. stimulus is transmitted from one side to the other in this array. The stimulus actively creates the ways to be transmitted, by making the chaotic elements to phase synchronize}, language = {en} } @article{ChenShiauTsengetal.2010, author = {Chen, Jin-Long and Shiau, Yuo-Hsien and Tseng, Yin-Jiun and Chiu, Hung-Wen and Hsiao, Tzu-Chien and Wessel, Niels and Kurths, J{\"u}rgen and Chu, Woei-Chyn}, title = {Concurrent sympathetic activation and vagal withdrawal in hyperthyroidism : evidence from detrended fluctuation analysis of heart rate variability}, issn = {0378-4371}, doi = {10.1016/j.physa.2009.12.062}, year = {2010}, abstract = {Despite many previous Studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance related to the autonomic nervous system. In particular, an increased short-term scaling exponent alpha 1 calculated from DFA is associated with both increased sympathetic activity and decreased vagal activity. No study has investigated the DFA of HRV in hyperthyroidism. This study was designed to assess the sympathovagal balance in hyperthyroidism. We performed the DFA along with the linear analysis of HRV in 36 hyperthyroid Graves' disease patients (32 females and 4 males; age 30 +/- 1 years, means +/- SE) and 36 normal controls matched by sex, age and body mass index. Compared with the normal controls, the hyperthyroid patients revealed a significant increase (P < 0.001) in alpha 1 (hyperthyroid 1.28 +/- 0.04 versus control 0.91 +/- 0.02), long-term scaling exponent alpha 2 (1.05 +/- 0.02 versus 0.90 +/- 0.01), overall scaling exponent alpha (1.11 +/- 0.02 versus 0.89 +/- 0.01), low frequency power in normalized units (LF\%) and the ratio of low frequency power to high frequency power (LF/HF); and a significant decrease (P < 0.001) in the standard deviation of the R-R intervals (SDNN) and high frequency power (HF). In conclusion, hyperthyroidism is characterized by concurrent sympathetic activation and vagal withdrawal. This sympathovagal imbalance state in hyperthyroidism helps to explain the higher prevalence of atrial fibrillation and exercise intolerance among hyperthyroid patients.}, language = {en} } @book{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Characterizing the dynamics of stochastic bistable systems by measures of complexity}, series = {Preprint NLD}, volume = {36}, journal = {Preprint NLD}, publisher = {Univ. Potsdam}, address = {Potsdam}, issn = {1432-2935}, pages = {20 S. : graph. Darst.}, year = {1997}, language = {en} } @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{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{SunLuKurthsetal.2009, author = {Sun, Xiaojuan and Lu, Qishao and Kurths, J{\"u}rgen and Wang, Qingyun}, title = {Spatiotemporal coherence resonance in a map lattice}, issn = {0218-1274}, doi = {10.1142/S021812740902310X}, year = {2009}, abstract = {We study the effects of parametric noise on a lattice network, which is locally modeled by a two-dimensional Rulkov map. We conclude that at some intermediate noise intensity, parametric noise can induce ordered circular patterns, which indicates the appearance of spatiotemporal coherence resonance in the studied lattice. With the observation of coherence-like manner in linear spatial cross-correlation, the coherence phenomena can be analyzed quantitatively.}, language = {en} } @article{FujiwaraKurths2009, author = {Fujiwara, Naoya and Kurths, J{\"u}rgen}, title = {Spectral universality of phase synchronization in non-identical oscillator networks}, issn = {1434-6028}, doi = {10.1140/epjb/e2009-00078-6}, year = {2009}, abstract = {We employ a spectral decomposition method to analyze synchronization of a non-identical oscillator network. We study the case that a small parameter mismatch of oscillators is characterized by one parameter and phase synchronization is observed. We derive a linearized equation for each eigenmode of the coupling matrix. The parameter mismatch is reflected on inhomogeneous term in the linearized equation. We find that the oscillation of each mode is essentially characterized only by the eigenvalue of the coupling matrix with a suitable normalization. We refer to this property as spectral universality, because it is observed irrespective of network topology. Numerical results in various network topologies show good agreement with those based on linearized equation. This universality is also observed in a system driven by additive independent Gaussian noise.}, language = {en} } @article{KoseskaVolkovKurths2009, author = {Koseska, Aneta and Volkov, Evgenij and Kurths, J{\"u}rgen}, title = {Detuning-dependent dominance of oscillation death in globally coupled synthetic genetic oscillators}, issn = {0295-5075}, doi = {10.1209/0295-5075/85/28002}, year = {2009}, abstract = {We study dynamical regimes of globally coupled genetic relaxation oscillators in the presence of small detuning. Using bifurcation analysis, we find that under strong coupling via the slow variable, the detuning can eliminate standard oscillatory solutions in a large region of the parameter space, providing the dominance of oscillation death. This result is substantially different from previous results on oscillation quenching, where for homogeneous populations, the coexistence of oscillation death and limit cycle oscillations is always present. We propose further that this effect of detuning-dependent dominance could be a powerful regulator of genetic network's dynamics.}, language = {en} } @article{ZhouKurths2006, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Hierarchical synchronization in complex networks with heterogeneous degrees}, issn = {1054-1500}, doi = {10.1063/1.2150381}, year = {2006}, abstract = {We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. (C) 2006 American Institute of Physics}, language = {en} } @article{WittFeudelGebogietal.1998, author = {Witt, Annette and Feudel, Fred and Gebogi, C. and Kurths, J{\"u}rgen and Braun, Robert}, title = {Tracer dynamics in a flow of driven vortices}, series = {Preprint NLD}, volume = {51}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {8 S. : graph. Darst.}, year = {1998}, 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{ItohKurths2010, author = {Itoh, Naoki and Kurths, J{\"u}rgen}, title = {Change-point detection of climate time series by nonparametric method}, issn = {2078-0958}, year = {2010}, abstract = {In one of the data mining techniques, change-point detection is of importance in evaluating time series measured in real world. For decades this technique has been developed as a nonlinear dynamics. We apply the method for detecting the change points, Singular Spectrum Transformation (SST), to the climate time series. To know where the structures of climate data sets change can reveal a climate background. In this paper we discuss the structures of precipitation data in Kenya and Wrangel Island (Arctic land) by using the SST.}, language = {en} } @article{RetzlaffBauernschmittMalbergetal.2009, author = {Retzlaff, Beatrice and Bauernschmitt, Robert and Malberg, Hagen and Brockmann, Gernot and Uhl, Christian and Lange, Ruediger and Kurths, J{\"u}rgen and Bretthauer, Georg and Wessel, Niels}, title = {Depression of cardiovascular autonomic function is more pronounced after mitral valve surgery : evidence for direct trauma}, issn = {1364-503X}, doi = {10.1098/rsta.2008.0272}, year = {2009}, abstract = {The analysis of baroreflex sensitivity (BRS) and heart rate variability (HRV) leads to additional insights into patients' prognosis after cardiovascular events. The following study was performed to assess the differences in the post-operative recovery of autonomic regulation after mitral valve (MV) and aortic valve (AV) surgery with a heart lung machine. Among the 43 consecutive male patients enrolled in a prospective study, 26 underwent isolated AV surgery and 17 isolated MV surgery. Blood pressure as well as ECG signals were recorded the day before, 24 hours after and one week after surgery. BRS was calculated according to the dual sequence method, and HRV was calculated using standard linear as well as nonlinear parameters. There were no major differences between the two groups in the pre-operative values. At 24 hours a comparable depression of HRV and BRS in both groups was observed, while at 7 days there was partial recovery in AV patients, which was absent in MV patients: p(AV versus MV) < 0.001. While the response of the autonomic system to surgery is similar in AV and MV patients, there is obviously a decreased ability to recover in MV patients, probably attributed to traumatic lesions of the autonomic nervous system by opening the atria. Ongoing research is required for further clarification of the pathophysiology of this phenomenon and to establish strategies to restore autonomic function.}, language = {en} } @article{PavlovAnisimovSemyachkinaGlushkovskayaetal.2009, author = {Pavlov, Alexey N. and Anisimov, A. A. and Semyachkina-Glushkovskaya, Oxana V. and Matasova, E. G. and Kurths, J{\"u}rgen}, title = {Analysis of blood pressure dynamics in male and female rats using the continuous wavelet transform}, issn = {0967-3334}, doi = {10.1088/0967-3334/30/7/013}, year = {2009}, abstract = {We study gender-related particularities in cardiovascular responses to stress and nitric oxide (NO) deficiency in rats using HR, mean arterial pressure (MAP) and a proposed wavelet-based approach. Blood pressure dynamics is analyzed: (1) under control conditions, (2) during immobilization stress and recovery and (3) during nitric oxide blockade by N-G-nitro-L-arginine-methyl ester (L-NAME). We show that cardiovascular sensitivity to stress and NO deficiency depends upon gender. Actually, in females the chronotropic effect of stress is more pronounced, while the pressor effect is weakened compared with males. We conclude that females demonstrate more favorable patterns of cardiovascular responses to stress and more effective NO control of cardiovascular activity than males.}, language = {en} } @article{PereiraBaptistaReyesetal.2009, author = {Pereira, Tiago and Baptista, Murilo da Silva and Reyes, Marcelo B. and Caldas, Ibere Luiz and Sartorelli, Jos{\´e} Carlos and Kurths, J{\"u}rgen}, title = {A scenario for torus T-2 destruction via a global bifurcation}, issn = {0960-0779}, doi = {10.1016/j.chaos.2007.06.115}, year = {2009}, abstract = {We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T-2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type- if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws.}, language = {en} } @article{RomanoThielKurthsetal.2009, author = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and Mergenthaler, Konstantin and Engbert, Ralf}, title = {Hypothesis test for synchronization : twin surrogates revisited}, issn = {1054-1500}, doi = {10.1063/1.3072784}, year = {2009}, abstract = {The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes.}, language = {en} } @article{RusconiVallerianiDunlopetal.2009, author = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard}, title = {Insights into the control of trabecular bone remodelling obtained by a Markov model}, issn = {8756-3282}, doi = {10.1016/j.bone.2009.03.467}, year = {2009}, language = {en} } @article{PortaDiRienzoWesseletal.2009, author = {Porta, Alberto and Di Rienzo, Marco and Wessel, Niels and Kurths, J{\"u}rgen}, title = {Addressing the complexity of cardiovascular regulation}, issn = {1364-503X}, doi = {10.1098/rsta.2008.0292}, year = {2009}, 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{VossKurths1998, author = {Voss, Henning U. and Kurths, J{\"u}rgen}, title = {Test for nonlinear dynamical behavior in symbol sequences}, year = {1998}, 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{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Charakterizing the dynamics of stochastic bistable systems by measures of complexity}, year = {1997}, 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} } @book{FeudelKurthsNeiman1995, author = {Feudel, Ulrike and Kurths, J{\"u}rgen and Neiman, Alexander}, title = {The cumulant approach for investigating the noise influence on mode-locking bifurcations}, series = {Preprint NLD}, volume = {16}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {20 S.}, year = {1995}, language = {en} }