@article{ZaikinKurths2006,
  author    = {Zaikin, Alexey and Kurths, J{\"u}rgen},
  title     = {Optimal length transportation hypothesis to model proteasome product size distribution},
  series = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences},
  volume    = {32},
  journal   = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences},
  number    = {3-4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0092-0606},
  doi       = {10.1007/s10867-006-9014-z},
  pages     = {231 -- 243},
  year      = {2006},
  abstract  = {This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport.},
  language  = {en}
}
@article{WuZhouChenetal.2010,
  author    = {Wu, Ye and Zhou, Changsong and Chen, Maoyin and Xiao, Jinghua and Kurths, J{\"u}rgen},
  title     = {Human comment dynamics in on-line social systems},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2010.08.049},
  year      = {2010},
  abstract  = {Human comment is studied using data from 'tianya' which is one of the most popular on-line social systems in China. We found that the time interval between two consecutive comments on the same topic, called inter-event time, follows a power-law distribution. This result shows that there is no characteristic decay time on a topic. It allows for very long periods without comments that separate bursts of intensive comments. Furthermore, the frequency of a different ID commenting on a topic also follows a power-law distribution. It indicates that there are some "hubs" in the topic who lead the direction of the public opinion. Based on the personal comments habit, a model is introduced to explain these phenomena. The numerical simulations of the model fit well with the empirical results. Our findings are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society.},
  language  = {en}
}
@article{WinterhalderSchelterKurthsetal.2006,
  author    = {Winterhalder, Matthias and Schelter, B and Kurths, J{\"u}rgen and Schulze-Borthage, A and Timmer, Jens},
  title     = {Sensitivity and specificity of coherence and phase synchronization analysis},
  doi       = {10.1016/j.physleta.2006.03.018},
  year      = {2006},
  abstract  = {In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{DanaBlasiusKurths2006,
  author    = {Dana, Syamal Kumar and Blasius, Bernd and Kurths, J{\"u}rgen},
  title     = {Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators},
  issn      = {1054-1500},
  doi       = {10.1063/1.2197168},
  year      = {2006},
  abstract  = {We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models},
  language  = {en}
}
@article{VasconcelosLopesVianaetal.2006,
  author    = {Vasconcelos, D. B. and Lopes, S. R. and Viana, R. L. and Kurths, J{\"u}rgen},
  title     = {Spatial recurrence plots},
  doi       = {10.1103/Physreve.73.056207},
  year      = {2006},
  abstract  = {We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes},
  language  = {en}
}
@article{BaptistaPereiraKurths2006,
  author    = {Baptista, Murilo da Silva and Pereira, Tiago and Kurths, J{\"u}rgen},
  title     = {Upper bounds in phase synchronous weak coherent chaotic attractors},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2006.02.007},
  year      = {2006},
  abstract  = {An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.},
  language  = {en}
}
@article{BaptistaPereiraSartorellietal.2005,
  author    = {Baptista, Murilo da Silva and Pereira, Tiago and Sartorelli, J. C. and Caldas, Ibere Luiz and Kurths, J{\"u}rgen},
  title     = {Non-transitive maps in phase synchronization},
  year      = {2005},
  abstract  = {Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{KitajimaKurths2005,
  author    = {Kitajima, H. and Kurths, J{\"u}rgen},
  title     = {Synchronized firing of FitzHugh-Nagumo neurons by noise},
  issn      = {1054-1500},
  year      = {2005},
  abstract  = {We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons. (C) 2005 American Institute of Physics},
  language  = {en}
}
@article{BeimGrabenFrischFinketal.2005,
  author    = {Beim Graben, Peter and Frisch, Stefan and Fink, A. and Saddy, Douglas and Kurths, J{\"u}rgen},
  title     = {Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event- related brain potentials (ERPs) in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio (SNR) for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component (the N400) against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so},
  language  = {en}
}
@article{MeineckeZieheKurthsetal.2005,
  author    = {Meinecke, Frank C. and Ziehe, Andreas and Kurths, J{\"u}rgen and M{\"u}ller, Klaus-Robert},
  title     = {Measuring phase synchronization of superimposed signals},
  issn      = {0031-9007},
  year      = {2005},
  abstract  = {Phase synchronization is an important phenomenon that occurs in a wide variety of complex oscillatory processes. Measuring phase synchronization can therefore help to gain fundamental insight into nature. In this Letter we point out that synchronization analysis techniques can detect spurious synchronization, if they are fed with a superposition of signals such as in electroencephalography or magnetoencephalography data. We show how techniques from blind source separation can help to nevertheless measure the true synchronization and avoid such pitfalls},
  language  = {en}
}
@article{SurovyatkinaKravtsovKurths2005,
  author    = {Surovyatkina, E. D. and Kravtsov, Y. A. and Kurths, J{\"u}rgen},
  title     = {Fluctuation growth and saturation in nonlinear oscillators on the threshold of bifurcation of spontaneous symmetry breaking},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We study prebifurcation fluctuation amplification in nonlinear oscillators subject to bifurcations of spontaneous symmetry breaking which are manifest in the doubling of stable equilibrium states. Our theoretical estimates of both the linear growth and the nonlinear saturation of the fluctuations are in good agreement with our results from numerical simulations. We show that in the saturation mode, the fluctuation variance is proportional to the standard deviation of the external noise, whereas in the linear mode, the fluctuation variance is proportional to the noise variance. It is demonstrated that the phenomenon of prebifurcation noise amplification is more pronounced in the case of a slow transition through the bifurcation point. The amplification of fluctuations in this case makes it easier to form a symmetric probability of the final equilibrium states. In contrast, for a fast transition through the bifurcation point, the effect of amplification is much less pronounced. Under backward and forward passages through the bifurcation point, a loop of noise-dependent hysteresis emerges here. We find that for a fast transition of the nonlinear oscillator through the bifurcation point, the probability symmetry of the final equilibrium states is destroyed},
  language  = {en}
}
@article{ShabuninAstakhovKurths2005,
  author    = {Shabunin, A. and Astakhov, Vladimir V. and Kurths, J{\"u}rgen},
  title     = {Quantitative analysis of chaotic synchronization by means of coherence},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We use an index of chaotic synchronization based on the averaged coherence function for the quantitative analysis of the process of the complete synchronization loss in unidirectionally coupled oscillators and maps. We demonstrate that this value manifests different stages of the synchronization breaking. It is invariant to time delay and insensitive to small noise and distortions, which can influence the accessible signals at measurements. Peculiarities of the synchronization destruction in maps and oscillators are investigated},
  language  = {en}
}
@article{SaparinThomsenProhaskaetal.2005,
  author    = {Saparin, P. I. and Thomsen, J. S. and Prohaska, Steffen and Zaikin, Alexei and Kurths, J{\"u}rgen and Hege, H. C. and Gowin, W.},
  title     = {Quantification of spatial structure of human proximal tibial bone biopsies using 3D measures of complexity},
  issn      = {0094-5765},
  year      = {2005},
  abstract  = {Changes in trabecular bone composition during development of osteoporosis are used as a model for bone loss in microgravity conditions during a space flight. Symbolic dynamics and measures of complexity are proposed and applied to assess quantitatively the structural composition of bone tissue from 3D data sets of human tibia bone biopsies acquired by a micro-CT scanner. In order to justify the newly proposed approach, the measures of complexity of the bone architecture were compared with the results of traditional 2D bone histomorphometry. The proposed technique is able to quantify the structural loss of the bone tissue and may help to diagnose and to monitor changes in bone structure of patients on Earth as well as of the space-flying personnel. © 2005 Elsevier Ltd. All rights reserved},
  language  = {en}
}
@article{SitzSchwarzKurths2004,
  author    = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {The unscented Kalman filter : a powerful tool for data analysis},
  year      = {2004},
  language  = {en}
}
@article{OrgisBrandSchwarzetal.2009,
  author    = {Orgis, Thomas and Brand, Sascha and Schwarz, Udo and Handorf, D{\"o}rthe and Dethloff, Klaus and Kurths, J{\"u}rgen},
  title     = {Influence of interactive stratospheric chemistry on large-scale air mass exchange in a global circulation model},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2009-01105-8},
  year      = {2009},
  abstract  = {A new globally uniform Lagrangian transport scheme for large ensembles of passive tracer particles is presented and applied to wind data from a coupled atmosphere-ocean climate model that includes interactive dynamical feedback with stratospheric chemistry. This feedback from the chemistry is found to enhance large-scale meridional air mass exchange in the northern winter stratosphere as well as intrusion of stratospheric air into the troposphere, where both effects are due to a weakened polar vortex.},
  language  = {en}
}
@article{RaabWesselSchirdewanetal.2006,
  author    = {Raab, Corinna and Wessel, Niels and Schirdewan, Alexander and Kurths, J{\"u}rgen},
  title     = {Large-scale dimension densities for heart rate variability analysis},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.73.041907},
  year      = {2006},
  abstract  = {In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification},
  language  = {en}
}
@article{AnishchenkoNikolaevKurths2006,
  author    = {Anishchenko, Vadim S. and Nikolaev, S and Kurths, J{\"u}rgen},
  title     = {Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.73.056202},
  year      = {2006},
  abstract  = {We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place},
  language  = {en}
}
@article{BoccalettiHwangChavezetal.2006,
  author    = {Boccaletti, Stefano and Hwang, Dong-Uk and Chavez, Mario and Amann, Andreas and Kurths, J{\"u}rgen and Pecora, Louis M.},
  title     = {Synchronization in dynamical networks : evolution along commutative graphs},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.74.016102},
  year      = {2006},
  abstract  = {Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior},
  language  = {en}
}
@article{ThielRomanoKurths2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen},
  title     = {Spurious structures in recurrence plots induced by embedding},
  doi       = {10.1007/s11071-006-2010-9},
  year      = {2006},
  abstract  = {In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay},
  language  = {en}
}
@article{LiSunKurths2006,
  author    = {Li, Changpin and Sun, Weigang and Kurths, J{\"u}rgen},
  title     = {Synchronization of complex dynamical networks with time delays},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2005.07.007},
  year      = {2006},
  abstract  = {In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems.},
  language  = {en}
}
@article{SchmidtZamoraLopezKurths2010,
  author    = {Schmidt, G. and Zamora-Lopez, Gorka and Kurths, J{\"u}rgen},
  title     = {Simulation of large scale cortical networks by individual neuron dynamics},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127410026149},
  year      = {2010},
  abstract  = {Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required.},
  language  = {en}
}
@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}
}