TY - GEN
A1 - Allefeld, Carsten
A1 - Kurths, Jürgen
T1 - Testing for phase synchronization
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 071
Y1 - 2004
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20091
ER -
TY - GEN
A1 - Allefeld, Carsten
A1 - Kurths, Jürgen
T1 - An approach to multivariate phase synchronization analysis and its application to event-related potentials
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 069
Y1 - 2004
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20106
ER -
TY - INPR
A1 - Engbert, Ralf
A1 - Scheffczyk, Christian
A1 - Krampe, Ralf-Thomas
A1 - Rosenblum, Mikhael
A1 - Kurths, Jürgen
A1 - Kliegl, Reinhold
T1 - Tempo-induced transitions in polyrhythmic hand movements
N2 - 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.
T3 - NLD Preprints - paper 041
Y1 - 1997
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14380
ER -
TY - INPR
A1 - Witt, Annette
A1 - Neiman, Alexander
A1 - Kurths, Jürgen
T1 - Characterizing the dynamics of stochastic bistable systems by measures of complexity
N2 - 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.
T3 - NLD Preprints - paper 036
Y1 - 1997
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14556
ER -
TY - INPR
A1 - Voss, Henning
A1 - Kurths, Jürgen
A1 - Schwarz, Udo
T1 - Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis
N2 - 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.
T3 - NLD Preprints - paper 028
Y1 - 1996
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14083
ER -
TY - GEN
A1 - Thiel, Marco
A1 - Romano, Maria Carmen
A1 - Kurths, Jürgen
A1 - Rolfs, Martin
A1 - Kliegl, Reinhold
T1 - Generating Surrogates from Recurrences
N2 - 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.
T3 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe - paper 238
KW - Æ Recurrence Plots
KW - Surrogate Data
KW - Hypothesis Test
KW - Phase Synchronization
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56906
ER -
TY - GEN
A1 - Thiel, Marco
A1 - Romano, Maria Carmen
A1 - Kurths, Jürgen
A1 - Rolfs, Martin
T1 - Twin Surrogates to Test for Complex Synchronisation
N2 - 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.
T3 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe - paper 264
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57231
ER -