Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen
OPUS4-35734 Wissenschaftlicher Artikel Malik, Nishant; Bookhagen, Bodo; Marwan, Norbert; Kurths, Jürgen Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks We present a detailed analysis of summer monsoon rainfall over the Indian peninsular using nonlinear spatial correlations. This analysis is carried out employing the tools of complex networks and a measure of nonlinear correlation for point processes such as rainfall, called event synchronization. This study provides valuable insights into the spatial organization, scales, and structure of the 90th and 94th percentile rainfall events during the Indian summer monsoon (June-September). We furthermore analyse the influence of different critical synoptic atmospheric systems and the impact of the steep Himalayan topography on rainfall patterns. The presented method not only helps us in visualising the structure of the extreme-event rainfall fields, but also identifies the water vapor pathways and decadal-scale moisture sinks over the region. Furthermore a simple scheme based on complex networks is presented to decipher the spatial intricacies and temporal evolution of monsoonal rainfall patterns over the last 6 decades. New York Springer 2012 17 Climate dynamics : observational, theoretical and computational research on the climate system 39 3-4 971 987 10.1007/s00382-011-1156-4 Institut für Physik und Astronomie
OPUS4-10612 Wissenschaftlicher Artikel Thiel, Marco; Romano, Maria Carmen; Kurths, Jürgen; Rolfs, Martin; Kliegl, Reinhold Generating surrogates from recurrences In this paper, we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres. 2008 Institut für Psychologie
OPUS4-13471 Wissenschaftlicher Artikel Baptista, Murilo S.; Pereira, Tiago; Sartorelli, J. C.; Caldas, I. L.; Kurths, Jürgen Non-transitive maps in phase synchronization 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 2005 Institut für Physik und Astronomie
OPUS4-19930 Wissenschaftlicher Artikel Landa, Polina S.; Zaikin, Alexei A.; Ushakov, V. G.; Kurths, Jürgen Influence of additive noise on transitions in nonlinear systems The effect of additive noise on transitions in nonlinear systems far from equilibrium is studied. It is shown that additive noise in itself can induce a hidden phase transition, which is similar to the transition induced by multiplicative noise in a nonlinear oscillator [P. Landa and A. Zaikin, Phys. Rev. E 54, 3535 (1996)]. Investigation of different nonlinear models that demonstrate phase transitions induced by multiplicative noise shows that the influence of additive noise upon such phase transitions can be crucial: additive noise can either blur such a transition or stabilize noise-induced oscillations. 2000 Institut für Physik und Astronomie
OPUS4-21090 Wissenschaftlicher Artikel Zaks, Michael A.; Pikovskij, Arkadij S.; Kurths, Jürgen On the generalized dimensions for the fourier spectrum of the thue-morse sequence 1999 Institut für Physik und Astronomie
OPUS4-18766 Wissenschaftlicher Artikel Gowin, W.; Saparin, Peter; Kurths, Jürgen; Felsenberg, D. Bone Architecture assessment with Measures of Complexity 2001 Institut für Physik und Astronomie
OPUS4-13583 Wissenschaftlicher Artikel Feudel, Fred; Witt, Annette; Gellert, Marcus; Kurths, Jürgen; Grebogi, Celso; Sanjuan, Miguel Angel Fernandez Intersections of stable and unstable manifolds : the skeleton of Lagrangian chaos 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 2005 Institut für Physik und Astronomie
OPUS4-16964 Wissenschaftlicher Artikel Sitz, Andre; Schwarz, Udo; Kurths, Jürgen; Voss, Henning U. Estimation of parameters and unobserved components for nonlinear systems from noisy time series 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. 2002 Institut für Physik und Astronomie
OPUS4-23952 Wissenschaftlicher Artikel Spahn, Frank; Schwarz, Udo; Kurths, Jürgen Clustering of granular assemblies with temperature dependent restitution under Keplerian differential rotation 1997 Institut für Physik und Astronomie
OPUS4-21962 Wissenschaftlicher Artikel Schwache, A.; Kurths, Jürgen; Mitschke, F.; Voss, Henning U. Equations of motion from chaotic data : a driven optical fiber ring resonator 1999 Institut für Physik und Astronomie
OPUS4-17559 Wissenschaftlicher Artikel Zhou, Changsong; Kurths, Jürgen; Kiss, Istvan Z.; Hudson, J. L. Noise-enhanced phase synchronization of chaotic oscillators 2002 Institut für Physik und Astronomie
OPUS4-1827 misc Allefeld, Carsten; Kurths, Jürgen Testing for phase synchronization 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. 2004 urn:nbn:de:kobv:517-opus-20091 Institut für Physik und Astronomie
OPUS4-38197 Wissenschaftlicher Artikel Goswami, Bedatha; Heitzig, Jobst; Rehfeld, Kira; Marwan, Norbert; Anoop, Ambili; Prasad, Sushma; Kurths, Jürgen Estimation of sedimentary proxy records together with associated uncertainty Sedimentary proxy records constitute a significant portion of the recorded evidence that allows us to investigate paleoclimatic conditions and variability. However, uncertainties in the dating of proxy archives limit our ability to fix the timing of past events and interpret proxy record intercomparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively little focus has been placed on the propagation of the age (and radiocarbon calibration) uncertainties into the final proxy record. We present a generic Bayesian framework to estimate proxy records along with their associated uncertainty, starting with the radiometric age-depth and proxy-depth measurements, and a radiometric calibration curve if required. We provide analytical expressions for the posterior proxy probability distributions at any given calendar age, from which the expected proxy values and their uncertainty can be estimated. We illustrate our method using two synthetic data sets and then use it to construct the proxy records for groundwater inflow and surface erosion from Lonar lake in central India. Our analysis reveals interrelations between the uncertainty of the proxy record over time and the variance of proxies along the depth of the archive. For the Lonar lake proxies, we show that, rather than the age uncertainties, it is the proxy variance combined with calibration uncertainty that accounts for most of the final uncertainty. We represent the proxy records as probability distributions on a precise, error-free timescale that makes further time series analyses and intercomparisons of proxies relatively simple and clear. Our approach provides a coherent understanding of age uncertainties within sedimentary proxy records that involve radiometric dating. It can be potentially used within existing age modeling structures to bring forth a reliable and consistent framework for proxy record estimation. Göttingen Copernicus 2014 19 Nonlinear processes in geophysics 21 6 1093 1111 10.5194/npg-21-1093-2014 Institut für Erd- und Umweltwissenschaften
OPUS4-38567 Wissenschaftlicher Artikel Boers, Niklas; Barbosa, Henrique M. J.; Bookhagen, Bodo; Marengo, Jose A.; Marwan, Norbert; Kurths, Jürgen Propagation of Strong Rainfall Events from Southeastern South America to the Central Andes Based on high-spatiotemporal-resolution data, the authors perform a climatological study of strong rainfall events propagating from southeastern South America to the eastern slopes of the central Andes during the monsoon season. These events account for up to 70% of total seasonal rainfall in these areas. They are of societal relevance because of associated natural hazards in the form of floods and landslides, and they form an intriguing climatic phenomenon, because they propagate against the direction of the low-level moisture flow from the tropics. The responsible synoptic mechanism is analyzed using suitable composites of the relevant atmospheric variables with high temporal resolution. The results suggest that the low-level inflow from the tropics, while important for maintaining sufficient moisture in the area of rainfall, does not initiate the formation of rainfall clusters. Instead, alternating low and high pressure anomalies in midlatitudes, which are associated with an eastward-moving Rossby wave train, in combination with the northwestern Argentinean low, create favorable pressure and wind conditions for frontogenesis and subsequent precipitation events propagating from southeastern South America toward the Bolivian Andes. Boston American Meteorological Soc. 2015 18 Journal of climate 28 19 7641 7658 10.1175/JCLI-D-15-0137.1 Institut für Erd- und Umweltwissenschaften
OPUS4-37214 Wissenschaftlicher Artikel Donges, Jonathan Friedmann; Donner, Reik Volker; Rehfeld, K.; Marwan, Norbert; Trauth, Martin H.; Kurths, Jürgen Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks - a recently developed approach - are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods. Göttingen Copernicus 2011 18 Nonlinear processes in geophysics 18 5 545 562 10.5194/npg-18-545-2011 Institut für Geowissenschaften
OPUS4-38208 Wissenschaftlicher Artikel Stolbova, Veronika; Martin, P.; Bookhagen, Bodo; Marwan, Norbert; Kurths, Jürgen Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka This paper employs a complex network approach to determine the topology and evolution of the network of extreme precipitation that governs the organization of extreme rainfall before, during, and after the Indian Summer Monsoon (ISM) season. We construct networks of extreme rainfall events during the ISM (June-September), post-monsoon (October-December), and pre-monsoon (March-May) periods from satellite-derived (Tropical Rainfall Measurement Mission, TRMM) and rain-gauge interpolated (Asian Precipitation Highly Resolved Observational Data Integration Towards the Evaluation of Water Resources, APHRODITE) data sets. The structure of the networks is determined by the level of synchronization of extreme rainfall events between different grid cells throughout the Indian subcontinent. Through the analysis of various complex-network metrics, we describe typical repetitive patterns in North Pakistan (NP), the Eastern Ghats (EG), and the Tibetan Plateau (TP). These patterns appear during the pre-monsoon season, evolve during the ISM, and disappear during the post-monsoon season. These are important meteorological features that need further attention and that may be useful in ISM timing and strength prediction. Göttingen Copernicus 2014 17 Nonlinear processes in geophysics 21 4 901 917 10.5194/npg-21-901-2014 Institut für Erd- und Umweltwissenschaften
OPUS4-1238 unpublished Thiessenhusen, Kai-Uwe; Esposito, Larry W.; Kurths, Jürgen; Spahn, Frank Detection of hidden resonances in Saturn's B-ring 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. 1995 urn:nbn:de:kobv:517-opus-13618 Institut für Physik und Astronomie
OPUS4-32458 Wissenschaftlicher Artikel Zhou, Changsong; Kurths, Jürgen Dynamical weights and enhanced synchronization in adaptive complex networks 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 2006 10.1103/Physrevlett.96.164102 Institut für Physik und Astronomie
OPUS4-4329 misc Koseska, Aneta; Zaikin, Alexey; Kurths, Jürgen; García-Ojalvo, Jordi Timing cellular decision making under noise via cell-cell communication 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. 2009 urn:nbn:de:kobv:517-opus-45260 Institut für Physik und Astronomie
OPUS4-36734 Wissenschaftlicher Artikel Hempel, Sabrina; Koseska, Aneta; Nikoloski, Zoran; Kurths, Jürgen Unraveling gene regulatory networks from time-resolved gene expression data - a measures comparison study Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices. London BioMed Central 2011 26 BMC bioinformatics 12 1 10.1186/1471-2105-12-292 Institut für Biochemie und Biologie
OPUS4-37047 Wissenschaftlicher Artikel Grimbs, Sergio; Arnold, Anne; Koseska, Aneta; Kurths, Jürgen; Selbig, Joachim; Nikoloski, Zoran Spatiotemporal dynamics of the Calvin cycle multistationarity and symmetry breaking instabilities The possibility of controlling the Calvin cycle has paramount implications for increasing the production of biomass. Multistationarity, as a dynamical feature of systems, is the first obvious candidate whose control could find biotechnological applications. Here we set out to resolve the debate on the multistationarity of the Calvin cycle. Unlike the existing simulation-based studies, our approach is based on a sound mathematical framework, chemical reaction network theory and algebraic geometry, which results in provable results for the investigated model of the Calvin cycle in which we embed a hierarchy of realistic kinetic laws. Our theoretical findings demonstrate that there is a possibility for multistationarity resulting from two sources, homogeneous and inhomogeneous instabilities, which partially settle the debate on multistability of the Calvin cycle. In addition, our tractable analytical treatment of the bifurcation parameters can be employed in the design of validation experiments. Oxford Elsevier 2011 12 Biosystems : journal of biological and information processing sciences 103 2 212 223 10.1016/j.biosystems.2010.10.015 Institut für Biochemie und Biologie
OPUS4-31446 Wissenschaftlicher Artikel Zakharova, Anna; Vadivasova, Tatjana; Anishchenko, Vadim S.; Koseska, Aneta; Kurths, Jürgen Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs. 2010 10.1103/Physreve.81.011106 Institut für Physik und Astronomie
OPUS4-36845 Wissenschaftlicher Artikel Zakharova, Anna; Kurths, Jürgen; Vadivasova, Tatyana; Koseska, Aneta Analysing dynamical behavior of cellular networks via stochastic bifurcations The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types. San Fransisco PLoS 2011 12 PLoS one 6 5 10.1371/journal.pone.0019696 Institut für Physik und Astronomie
OPUS4-15383 Wissenschaftlicher Artikel Thiel, M.; Romano, Maria Carmen; Read, P. L.; Kurths, Jürgen Estimation of dynamical invariants without embedding by recurrence plots 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 2004 Institut für Physik und Astronomie
OPUS4-36361 Wissenschaftlicher Artikel Rusconi, Marco; Valleriani, Angelo; Dunlop, John William Chapman; Kurths, Jürgen; Weinkamer, Richard Quantitative approach to the stochastics of bone remodeling During life bones constantly adapt their structure to their mechanical environment via a mechanically controlled process called bone remodeling. For trabecular bone, this process modifies the thickness of each trabecula leading occasionally to full resorption. We describe the irreversible dynamics of the trabecular thickness distribution (TTD) by means of a Markov chain discrete in space and time. By using thickness data from adult patients, we derive the transition probabilities in the chain. This allows a quantification, in terms of geometrical quantities, of the control of bone remodeling and thus to determine the evolution of the TTD with age. Mulhouse EDP Sciences 2012 6 epl : a letters journal exploring the frontiers of physics 97 2 10.1209/0295-5075/97/28009 Institut für Physik und Astronomie
OPUS4-36576 Wissenschaftlicher Artikel Koseska, Aneta; Volkov, Evgenii; Kurths, Jürgen Synthetic multicellular oscillatory systems controlling protein dynamics with genetic circuits Synthetic biology is a relatively new research discipline that combines standard biology approaches with the constructive nature of engineering. Thus, recent efforts in the field of synthetic biology have given a perspective to consider cells as 'programmable matter'. Here, we address the possibility of using synthetic circuits to control protein dynamics. In particular, we show how intercellular communication and stochasticity can be used to manipulate the dynamical behavior of a population of coupled synthetic units and, in this manner, finely tune the expression of specific proteins of interest, e.g. in large bioreactors. Bristol IOP Publ. Ltd. 2011 10 Physica scripta : an international journal for experimental and theoretical physics 84 4 10.1088/0031-8949/84/04/045007 Institut für Physik und Astronomie
OPUS4-31739 Wissenschaftlicher Artikel Koseska, Aneta; Volkov, Evgenij; Kurths, Jürgen Detuning-dependent dominance of oscillation death in globally coupled synthetic genetic oscillators 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. 2009 10.1209/0295-5075/85/28002 Institut für Physik und Astronomie
OPUS4-36730 Wissenschaftlicher Artikel Hempel, Stefan; Koseska, Aneta; Kurths, Jürgen; Nikoloski, Zoran Inner composition alignment for inferring directed networks from short time series Identifying causal links (couplings) is a fundamental problem that facilitates the understanding of emerging structures in complex networks. We propose and analyze inner composition alignment-a novel, permutation-based asymmetric association measure to detect regulatory links from very short time series, currently applied to gene expression. The measure can be used to infer the direction of couplings, detect indirect (superfluous) links, and account for autoregulation. Applications to the gene regulatory network of E. coli are presented. College Park American Physical Society 2011 4 Physical review letters 107 5 10.1103/PhysRevLett.107.054101 Institut für Biochemie und Biologie
OPUS4-1334 unpublished Engbert, Ralf; Scheffczyk, Christian; Krampe, Ralf-Thomas; Rosenblum, Mikhael; Kurths, Jürgen; Kliegl, Reinhold Tempo-induced transitions in polyrhythmic hand movements We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components. 1997 urn:nbn:de:kobv:517-opus-14380 Institut für Psychologie
OPUS4-1325 unpublished Witt, Annette; Neiman, Alexander; Kurths, Jürgen Characterizing the dynamics of stochastic bistable systems by measures of complexity 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. 1997 urn:nbn:de:kobv:517-opus-14556 Institut für Physik und Astronomie
OPUS4-1372 unpublished Guasti, Giovanna; Engbert, Ralf; Krampe, Ralf T.; Kurths, Jürgen Phase transitions, complexity, and stationarity in the production of polyrhythms 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 2000 urn:nbn:de:kobv:517-opus-14933 Institut für Psychologie
OPUS4-17557 Wissenschaftlicher Artikel Boccaletti, Stefano; Kurths, Jürgen; Osipov, Grigory V. The synchronization of chaotic systems 2002 Institut für Physik und Astronomie
OPUS4-1254 unpublished Pikovsky, Arkady S.; Zaks, Michael A.; Feudel, Ulrike; Kurths, Jürgen Singular continuous spectra in dissipative dynamics We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique. 1995 urn:nbn:de:kobv:517-opus-13787 Institut für Physik und Astronomie
OPUS4-5489 misc Thiel, Marco; Romano, Maria Carmen; Kurths, Jürgen; Rolfs, Martin; Kliegl, Reinhold Generating Surrogates from Recurrences In this paper we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres. 2006 urn:nbn:de:kobv:517-opus-56906 Institut für Psychologie
OPUS4-5522 misc Thiel, Marco; Romano, Maria Carmen; Kurths, Jürgen; Rolfs, Martin Twin Surrogates to Test for Complex Synchronisation We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems. 2006 urn:nbn:de:kobv:517-opus-57231 Institut für Psychologie
OPUS4-20297 Wissenschaftlicher Artikel Hainzl, Sebastian; Zöller, Gert; Kurths, Jürgen; Zschau, Jochen Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality 2000 Institut für Physik und Astronomie
OPUS4-18765 Wissenschaftlicher Artikel Zöller, Gert; Hainzl, Sebastian; Kurths, Jürgen Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes 2001 Institut für Physik und Astronomie
OPUS4-21099 Wissenschaftlicher Artikel Hainzl, Sebastian; Zöller, Gert; Kurths, Jürgen Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes 1999 Institut für Physik und Astronomie
OPUS4-21115 Wissenschaftlicher Artikel Hainzl, Sebastian; Zöller, Gert; Kurths, Jürgen Self-organized criticality model for earthquakes : Quiescence, foreshocks and aftershocks 1999 Institut für Physik und Astronomie
OPUS4-23479 Wissenschaftlicher Artikel Engbert, Ralf; Hainzl, Sebastian; Zöller, Gert; Kurths, Jürgen Testing for unstable periodic orbits to characterize spatiotemporal dynamics 1998 Institut für Physik und Astronomie
OPUS4-20302 Wissenschaftlicher Artikel Hainzl, Sebastian; Zöller, Gert; Kurths, Jürgen Self-organization of spatio-temporal earthquake clusters 2000 Institut für Physik und Astronomie
OPUS4-32447 Wissenschaftlicher Artikel Thiel, Marco; Romano, Maria Carmen; Kurths, Jürgen; Rolfs, Martin; Kliegl, Reinhold Twin surrogates to test for complex synchronisation We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of Rossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems 2006 10.1209/epl/i2006-10147-0 Department Psychologie
OPUS4-22402 Wissenschaftlicher Artikel Witt, Annette; Feudel, Fred; Gebogi, C.; Kurths, Jürgen; Braun, Robert Tracer dynamics in a flow of driven vortices Potsdam Univ. 1998 8 S. : graph. Darst. Preprint NLD 51 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-23940 Wissenschaftlicher Artikel Ruzick, Oliver; Scheffczyk, Christian; Pikovskij, Arkadij S.; Kurths, Jürgen Dynamics of chaos-order interface in coupled map lattices 1997 Institut für Physik und Astronomie
OPUS4-20303 Wissenschaftlicher Artikel Zaks, Michael A.; Park, Eun Hyoung; Kurths, Jürgen On phase synchronization by periodic force in chaotic oscillators with saddle equilibria 2000 Institut für Physik und Astronomie
OPUS4-21339 Wissenschaftlicher Artikel Pikovskij, Arkadij S.; Rosenblum, Michael G.; Zaks, Michael A.; Kurths, Jürgen Phase synchronization of regular and chaotic oscillators 1999 Institut für Physik und Astronomie
OPUS4-21963 Wissenschaftlicher Artikel Braun, Robert; Feudel, Fred; Gebogi, C.; Kurths, Jürgen; Witt, Annette Tracer dynamics in a flow of driven vortices 1999 Institut für Physik und Astronomie
OPUS4-20299 Wissenschaftlicher Artikel Ziehmann, Christine; Smith, Leonard A.; Kurths, Jürgen Localized Lyapunov exponents and the prediction of predictability 2000 Institut für Physik und Astronomie
OPUS4-20300 Wissenschaftlicher Artikel Boccaletti, Stefano; Valladares, D. L.; Kurths, Jürgen Synchronization of chaotic structurally nonequivalent systems 2000 Institut für Physik und Astronomie
OPUS4-20298 Wissenschaftlicher Artikel Anishchenko, Vadim S.; Kopeikin, A. S.; Kurths, Jürgen Studying hyperbolicity in chaotic systems 2000 Institut für Physik und Astronomie
OPUS4-10999 Wissenschaftlicher Artikel Palus, Milan; Kurths, Jürgen; Schwarz, Udo; Seehafer, Norbert; Novotna, Dagmar; Charvatova, Ivanka The solar activity cycle is weakly synchronized with the solar inertial motion 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. 2007 10.1016/j.physleta.2007.01.039 Institut für Physik und Astronomie
OPUS4-15422 Wissenschaftlicher Artikel Zhou, Changsong; Kurths, Jürgen Resonant patterns in noisy active media 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 2004 Institut für Physik und Astronomie
OPUS4-23953 Buch (Monographie) Rosenblum, Michael G.; Schäfer, Carsten; Abel, Hans-Henning; Kurths, Jürgen Interrelationship of Parasympathetic Innervation of the Sinoatrial Node and the Atrioventricular Node of Human Heart 1997 Institut für Physik und Astronomie
OPUS4-34319 Wissenschaftlicher Artikel Romano, Maria Carmen; Thiel, Marco; Kurths, Jürgen; Rolfs, Martin; Engbert, Ralf; Kliegl, Reinhold Synchronization Analysis and Recurrence in Complex Systems 2006 978-3-527-40623-4 Institut für Psychologie
OPUS4-24207 Buch (Monographie) Witt, Annette; Neiman, Alexander; Kurths, Jürgen Characterizing the dynamics of stochastic bistable systems by measures of complexity Potsdam Univ. Potsdam 1997 20 S. : graph. Darst. Preprint NLD 36 Institut für Physik und Astronomie
OPUS4-18223 Buch (Monographie) Pikovskij, Arkadij S.; Rosenblum, Michael G.; Kurths, Jürgen Synchronization : a universal concept in nonlinear sciences 1st paperback ed., repr Cambridge Cambridge Univ. Press 2001 XIX, 411 S. : Ill., graph. Darst. Cambridge nonlinear science series 12 0-521-59285-2 Institut für Physik und Astronomie
OPUS4-22696 Buch (Monographie) Kurths, Jürgen; Mayer-Kress, Gottfried Kantz, Holger Nonlinear analysis of physiological data Berlin, New York Springer 1998 VIII, 344 S. : Ill., graph. Darst. 3-540-63481-9 Institut für Physik und Astronomie
OPUS4-1227 unpublished Kurths, Jürgen; Voss, A.; Witt, Annette; Saparin, P.; Kleiner, H. J.; Wessel, N. Quantitative analysis of heart rate variability 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. 1994 urn:nbn:de:kobv:517-opus-13470 Institut für Physik und Astronomie
OPUS4-32471 Wissenschaftlicher Artikel Zhou, Changsong; Kurths, Jürgen Hierarchical synchronization in complex networks with heterogeneous degrees 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 2006 10.1063/1.2150381 Institut für Physik und Astronomie
OPUS4-32374 Wissenschaftlicher Artikel Schelter, Björn; Winterhalder, Matthias; Dahlhaus, Rainer; Kurths, Jürgen; Timmer, Jens Partial phase synchronization for multivariate synchronizing systems 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 2006 10.1103/Physrevlett.96.208103 Institut für Physik und Astronomie
OPUS4-18288 Wissenschaftlicher Artikel Romano, Maria Carmen; Thiel, Marco; Schwarz, Udo; Kurths, Jürgen; Lange, Holger; Hauhs, M. Conceptual model of runoff from a forested catchment We investigate the relationship between precipitation and runoff data from a small forested catchment in the Harz mountains (Germany). For this purpose, we develop a conceptual model including memory effects to predict the runoff signal using the precipitation data as input. An enhanced variant of the model also includes air temperature as input variable. We show in terms of correlation functions that this model describes main dynamical properties of the runoff, especially the delay between rain event and runoff response as the annual persistence in the runoff data. 2001 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-32459 Wissenschaftlicher Artikel Zhou, Changsong; Motter, Adilson E.; Kurths, Jürgen Universality in the synchronization of weighted random networks 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 2006 10.1103/Physrevlett.96.034101 Institut für Physik und Astronomie
OPUS4-31374 Wissenschaftlicher Artikel Baptista, Murilo S.; Zhou, Changsong; Kurths, Jürgen Information transmission in phase synchronous chaotic arrays 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 2006 10.1088/0256-307X/23/3/010 Institut für Physik und Astronomie
OPUS4-19927 Wissenschaftlicher Artikel Popovych, Orest; Maistrenko, Yu; Mosekilde, Erik; Pikovskij, Arkadij S.; Kurths, Jürgen Transcritical loss of synchronization in coupled chaotic systems 2000 Institut für Physik und Astronomie
OPUS4-1226 unpublished Witt, Annette; Kurths, Jürgen; Krause, F.; Fischer, K. On the validity of a model for the reversals of the Earth's magnetic field 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. 1994 urn:nbn:de:kobv:517-opus-13460 Institut für Physik und Astronomie
OPUS4-1225 unpublished Kurths, Jürgen; Pikovsky, Arkady S.; Scheffczyk, Christian Roughening interfaces in deterministic dynamics Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface. 1994 urn:nbn:de:kobv:517-opus-13447 Institut für Physik und Astronomie
OPUS4-35779 Wissenschaftlicher Artikel Frasca, Mattia; Bergner, Andre; Kurths, Jürgen; Fortuna, Luigi Bifurcations in a star-like network of Stuart-Landau oscillators In this paper, we analytically study a star motif of Stuart-Landau oscillators, derive the bifurcation diagram and discuss the different forms of synchronization arising in such a system. Despite the parameter mismatch between the central node and the peripheral ones, an analytical approach independent of the number of units in the system has been proposed. The approach allows to calculate the separatrices between the regions with distinct dynamical behavior and to determine the nature of the different transitions to synchronization appearing in the system. The theoretical analysis is supported by numerical results. Singapore World Scientific 2012 13 International journal of bifurcation and chaos : in applied sciences and engineering 22 7 10.1142/S0218127412501738 Institut für Physik und Astronomie
OPUS4-41827 misc Agarwal, Ankit; Marwan, Norbert; Rathinasamy, Maheswaran; Merz, Bruno; Kurths, Jürgen Multi-scale event synchronization analysis for unravelling climate processes The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales. 2017 13 Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe 661 urn:nbn:de:kobv:517-opus4-418274 10.25932/publishup-41827 Mathematisch-Naturwissenschaftliche Fakultät
OPUS4-1828 misc Allefeld, Carsten; Kurths, Jürgen An approach to multivariate phase synchronization analysis and its application to event-related potentials 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. 2004 urn:nbn:de:kobv:517-opus-20106 Institut für Physik und Astronomie
OPUS4-34892 Wissenschaftlicher Artikel Goswami, Bedartha; Marwan, Norbert; Feulner, Georg; Kurths, Jürgen How do global temperature drivers influence each other? We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations. Heidelberg Springer 2013 13 European physical journal special topics 222 3-4 861 873 10.1140/epjst/e2013-01889-8 Institut für Physik und Astronomie
OPUS4-26857 Wissenschaftlicher Artikel Kurths, Jürgen; Schwarz, Udo; Witt, Annette Non-linear data analysis in solar radio astronomy 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. 1995 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-24923 Wissenschaftlicher Artikel Zaks, Michael A.; Rosenblum, Michael G.; Pikovskij, Arkadij S.; Osipov, Grigory V.; Kurths, Jürgen Phase synchronization of chaotic oscillations in terms of periodic orbits 1997 Institut für Physik und Astronomie
OPUS4-11164 Buch (Monographie) Osipov, Grigory V.; Kurths, Jürgen; Zhou, Changsong Synchronisation in Oscillatory Networks Berlin Springer-Verlag 2007 368 S. 978-3-540-71268-8 Institut für Psychologie
OPUS4-11950 Wissenschaftlicher Artikel Wu, Ye; Zhou, Changsong; Chen, Maoying; Xiao, Jinghua; Kurths, Jürgen Human comment dynamics in on-line social systems 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. 2010 10.1016/j.physa.2010.08.049 Institut für Physik und Astronomie
OPUS4-12025 Wissenschaftlicher Artikel Kurths, Jürgen; Romano, Maria Carmen; Thiel, Marco; Osipov, Grigory V.; Ivanchenko, Mikhail V.; Kiss, Istvan Z.; Hudson, John L. Synchronization analysis of coupled noncoherent oscillators We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators 2006 10.1007/s11071-006-1957-x Institut für Physik und Astronomie
OPUS4-12045 Wissenschaftlicher Artikel Vasconcelos, D. B.; Lopes, S. R.; Viana, R. L.; Kurths, Jürgen Spatial recurrence plots 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 2006 10.1103/Physreve.73.056207 Institut für Physik und Astronomie
OPUS4-11962 Wissenschaftlicher Artikel Winterhalder, Matthias; Schelter, B; Kurths, Jürgen; Schulze-Borthage, A; Timmer, Jens Sensitivity and specificity of coherence and phase synchronization analysis 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 2006 10.1016/j.physleta.2006.03.018 Institut für Physik und Astronomie
OPUS4-40092 misc Hempel, Sabrina; Koseska, Aneta; Nikoloski, Zoran; Kurths, Jürgen Unraveling gene regulatory networks from time-resolved gene expression data Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices. 2017 26 urn:nbn:de:kobv:517-opus4-400924 Institut für Physik und Astronomie
OPUS4-32214 Wissenschaftlicher Artikel Helland, Vanessa Carolina Figuera; Gapelyuk, Andrej; Suhrbier, Alexander; Riedl, Maik; Penzel, Thomas; Kurths, Jürgen; Wessel, Niels Investigation of an automatic sleep stage classification by means of multiscorer hypnogram Objectives: Scoring sleep visually based on polysomnography is an important but time-consuming element of sleep medicine. Where-as computer software assists human experts in the assignment of sleep stages to polysomnogram epochs, their performance is usually insufficient. This study evaluates the possibility to fully automatize sleep staging considering the reliability of the sleep stages available from human expert sleep scorers. Methods: We obtain features from EEG, ECG and respiratory signals of polysomnograms from ten healthy subjects. Using the sleep stages provided by three human experts, we evaluate the performance of linear discriminant analysis on the entire polysomnogram and:only on epochs where the three experts agree in their-sleep stage scoring. Results: We show that in polysomnogram intervals, to which all three scorers assign the same sleep stage, our algorithm achieves 90% accuracy. This high rate of agreement with the human experts is accomplished with only a small set of three frequency features from the EEG. We increase-the performance to 93% by including ECG and respiration features. In contrast, on intervals of ambiguous sleep stage, the sleep stage classification obtained from our algorithm, agrees with the human consensus scorer in approximately 61%. Conclusions: These findings suggest that machine classification is highly consistent with human sleep staging and that error in the algorithm's assignments is rather a problem of lack of well-defined criteria for human experts to judge certain polysomnogram epochs than an insufficiency of computational procedures 2010 10.3414/Me09-02-0052 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31997 Wissenschaftlicher Artikel Wessel, Niels; Riedl, Maik; Kurths, Jürgen Is the normal heart rate "chaotic" due to respiration? 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?" 2009 10.1063/1.3133128 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-32023 Wissenschaftlicher Artikel Zolotova, Nadezhda V.; Ponyavin, Dmitri I.; Marwan, Norbert; Kurths, Jürgen Long-term asymmetry in the wings of the butterfly diagram Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator. 2009 10.1051/0004-6361/200811430 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-32017 Wissenschaftlicher Artikel Zamora-Lopez, Gorka; Zhou, Changsong; Kurths, Jürgen Graph analysis of cortical networks reveals complex anatomical communication substrate Sensory information entering the nervous system follows independent paths of processing such that specific features are individually detected. However, sensory perception, awareness, and cognition emerge from the combination of information. Here we have analyzed the corticocortical network of the cat, looking for the anatomical substrate which permits the simultaneous segregation and integration of information in the brain. We find that cortical communications are mainly governed by three topological factors of the underlying network: (i) a large density of connections, (ii) segregation of cortical areas into clusters, and (iii) the presence of highly connected hubs aiding the multisensory processing and integration. Statistical analysis of the shortest paths reveals that, while information is highly accessible to all cortical areas, the complexity of cortical information processing may arise from the rich and intricate alternative paths in which areas can influence each other. 2009 10.1063/1.3089559 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-32010 Wissenschaftlicher Artikel Wu, Ye; Li, Ping; Chen, Maoyin; Xiao, Jinghua; Kurths, Jürgen Response of scale-free networks with community structure to external stimuli 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. 2009 10.1016/j.physa.2009.03.037 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-32027 Wissenschaftlicher Artikel Schinkel, Stefan; Marwan, Norbert; Kurths, Jürgen Brain signal analysis based on recurrences The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to Such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis. 2009 10.1016/j.jphysparis.2009.05.007 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31646 Wissenschaftlicher Artikel Florence, Gerson; Dahlem, Markus A.; Almeida, Antônio-Carlos G.; Bassani, José W. M.; Kurths, Jürgen The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression : a computational study 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. 2009 10.1016/j.jtbi.2009.01.032 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31877 Wissenschaftlicher Artikel Riedl, Maik; van Leeuwen, Peter; Suhrbier, Alexander; Malberg, Hagen; Groenemeyer, Dietrich; Kurths, Jürgen; Wessel, Niels Testing foetal-maternal heart rate synchronization via model-based analyses The investigation of foetal reaction to internal and external conditions and stimuli is an important tool in the characterization of the developing neural integration of the foetus. An interesting example of this is the study of the interrelationship between the foetal and the maternal heart rate. Recent studies have shown a certain likelihood of occasional heart rate synchronization between mother and foetus. In the case of respiratory-induced heart rate changes, the comparison with maternal surrogates suggests that the evidence for detected synchronization is largely statistical and does not result from physiological interaction. Rather, they simply reflect a stochastic, temporary stability of two independent oscillators with time-variant frequencies. We reanalysed three datasets from that study for a more local consideration. Epochs of assumed synchronization associated with short-term regulation of the foetal heart rate were selected and compared with synchronization resulting from white noise instead of the foetal signal. Using data-driven modelling analysis, it was possible to identify the consistent influence of the heartbeat duration of maternal beats preceding the foetal beats during epochs of synchronization. These maternal beats occurred approximately one maternal respiratory cycle prior to the affected foetal beat. A similar effect could not be found in the epochs without synchronization. Simulations based on the fitted models led to a higher likelihood of synchronization in the data segments with assumed foetal-maternal interaction than in the segment without such assumed interaction. We conclude that the data-driven model-based analysis can be a useful tool for the identification of synchronization. 2009 10.1098/rsta.2008.0277 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31875 Wissenschaftlicher Artikel Retzlaff, Beatrice; Bauernschmitt, Robert; Malberg, Hagen; Brockmann, Gernot; Uhl, Christian; Lange, Ruediger; Kurths, Jürgen; Bretthauer, Georg; Wessel, Niels Depression of cardiovascular autonomic function is more pronounced after mitral valve surgery : evidence for direct trauma 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. 2009 10.1098/rsta.2008.0272 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31227 Wissenschaftlicher Artikel Braun, Holger; Ditlevsen, Peter D.; Kurths, Jürgen; Mudelsee, Manfred Limitations of red noise in analysing Dansgaard-Oeschger events During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions. 2010 10.5194/cp-6-85-2010 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31844 Wissenschaftlicher Artikel Pavlov, Alexey N.; Anisimov, A. A.; Semyachkina-Glushkovskaya, Oxana V.; Matasova, E. G.; Kurths, Jürgen Analysis of blood pressure dynamics in male and female rats using the continuous wavelet transform 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. 2009 10.1088/0967-3334/30/7/013 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31790 Wissenschaftlicher Artikel Marwan, Norbert; Kurths, Jürgen Comment on "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" by Rohde et al. : [Physica D 237 (2008) 619-629] In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process. 2009 10.1016/j.physd.2009.04.018 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31652 Wissenschaftlicher Artikel Fujiwara, Naoya; Kurths, Jürgen Spectral universality of phase synchronization in non-identical oscillator networks 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. 2009 10.1140/epjb/e2009-00078-6 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31897 Wissenschaftlicher Artikel Schinkel, Stefan; Marwan, Norbert; Dimigen, Olaf; Kurths, Jürgen Confidence bounds of recurrence-based complexity measures In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real- life data. 2009 10.1016/j.physleta.2009.04.045 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31860 Wissenschaftlicher Artikel Porta, Alberto; Di Rienzo, Marco; Wessel, Niels; Kurths, Jürgen Addressing the complexity of cardiovascular regulation 2009 10.1098/rsta.2008.0292 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-28926 Wissenschaftlicher Artikel Schwarz, udo; Benz, Arnold O.; Kurths, Jürgen; Witt, Annette Analysis of solar spike events by means of symbolic dynamics methods 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. 1993 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-28924 Wissenschaftlicher Artikel Kurths, Jürgen; Schwarz, Udo Application of techniques of nonlinear dynamics to SS Cyg 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. 1993 0-7503-0282-8 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-28117 Wissenschaftlicher Artikel Kurths, Jürgen; Schwarz, Udo Chaos theory and radio emission The application of chaos theory has become popular to understand the nature of various features of solar activity because most of them are far from regular. The usual approach, however, that is basing on finding low- dimensional structures of the underlying processes seems to be successful only in a few exceptional cases, such as in rather coherent phenomena as coronal pulsations. It is important to note that most phenomena in solar radio emission are more complex. We present two kinds of techniques from nonlinear dynamics which can be useful to analyse such phenomena: i] Fragmentation processes observed in solar spike events are studied by means of symbolic dynamics methods. Different measures of complexity calculated from such observations reveal that there is some order in this fragmentation. ii] Bursts are a typical transient phenomenon. To study energization processes causing impulsive microwave bursts, the wavelet analysis is applied. It exhibits structural differences of the pre- and post-impulsive phase in cases where the power spectra of both are not distinct. 1994 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-28118 Wissenschaftlicher Artikel Kurths, Jürgen; Schwarz, Udo; Parlitz, Ulrich; Sonett, Charles P. Testing for nonlinearity in radiocarbon data The radiocarbon record that has been extended from 7199 BC to 1891 AD is of fundamental importance to understand century-scale variations of solar activity. We have, therefore, studied how to extract information from dynamic reconstructions of this observational record. Using some rather unusual methods of nonlinear dynamics, we have found that the data are significantly different from linear colored noise and that there is some evidence of nonlinear behavior. The method of recurrence plots exhibits that the grand minima of solar activity are quite different in their recurrence. Most remarkably, it suggests that the recent epoch seems to be similar to the Medieval maximum. 1994 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-31226 Wissenschaftlicher Artikel Itoh, Naoki; Kurths, Jürgen Change-point detection of climate time series by nonparametric method 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. 2010 Interdisziplinäres Zentrum für Dynamik komplexer Systeme
OPUS4-42311 misc Goswami, Bedartha; Boers, Niklas; Rheinwalt, Aljoscha; Marwan, Norbert; Heitzig, Jobst; Breitenbach, Sebastian Franz Martin; Kurths, Jürgen Abrupt transitions in time series with uncertainties Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Nino-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon. 2018 10 Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe 576 urn:nbn:de:kobv:517-opus4-423111 10.25932/publishup-42311 Mathematisch-Naturwissenschaftliche Fakultät
OPUS4-1282 unpublished Voss, Henning; Kurths, Jürgen; Schwarz, Udo Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis 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. 1996 urn:nbn:de:kobv:517-opus-14083 Institut für Physik und Astronomie