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
OPUS4-34319 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
OPUS4-10612 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
OPUS4-15384 Wissenschaftlicher Artikel Thiel, M.; Romano, Maria Carmen; Schwarz, Udo; Kurths, Jürgen; Timmer, Jens Surrogate-based hypothesis test without surrogates Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1 2004 Institut für Physik und Astronomie
OPUS4-31882 Wissenschaftlicher Artikel Romano, Maria Carmen; Thiel, Marco; Kurths, Jürgen; Mergenthaler, Konstantin; Engbert, Ralf Hypothesis test for synchronization : twin surrogates revisited The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes. 2009 10.1063/1.3072784 Department Psychologie
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
OPUS4-15382 Wissenschaftlicher Artikel Thiel, M.; Romano, Maria Carmen; Kurths, Jürgen How much information is contained in a recurrence plot? Recurrence plots have recently been recognized as a powerful tool for the analysis of data. Not only the visualization of structures of the time series but also the possibility to estimate invariants from them and the possibility to analyze non-stationary data sets are remarkable. However, the question of how much information is encoded in such a two-dimensional and binary representation has not been discussed so far. In this Letter we show that-under some conditions-it is possible to reconstruct an attractor from the recurrence plot, at least topologically. This means that all relevant dynamical information is contained in the plot. (C) 2004 Elsevier B.V. All rights reserved 2004 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
OPUS4-15303 Wissenschaftlicher Artikel Romano, Maria Carmen; Thiel, Marco; Kurths, Jürgen; von Bloh, Werner Multivariate recurrence plots We propose a new approach to calculate recurrence plots of multivariate time series, based on joint recurrences in phase space. This new method allows to estimate dynamical invariants of the whole system, like the joint Renyi entropy of second order. We use this entropy measure to quantitatively study in detail the phase synchronization of two bidirectionally coupled chaotic systems and identify different types of transitions to chaotic phase synchronization in dependence on the coupling strength and the frequency mismatch. By means of this analysis we find several new phenomena, such a chaos-period-chaos transition to phase synchronization for rather large coupling strengths. (C) 2004 Elsevier B.V. All rights reserved 2004 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
OPUS4-18682 Wissenschaftlicher Artikel Thiel, Marco; Romano, Maria Carmen; Schwarz, Udo; Kurths, Jürgen; Hasinger, Günther; Belloni, Tomaso Nonlinear Time series analysis of the X-ray flux of compact objects We analyse the X-ray light curves of compact objects using linear and nonlinear time series analysis methods. A Power Density Spectrum (PDS) describes the overall second order properties of the observed data well. To look beyond we propose the nonlinear Q-statistic to detect an asymmetry of the time series. This allows us to find relevant time scales. This method even grants a subclassification of the known states of X-ray sources. 2001 Interdisziplinäres Zentrum für Dynamik komplexer Systeme