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  - Zweitveröffentlichungen 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  - Zweitveröffentlichungen 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  - 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  - Zweitveröffentlichungen 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  - Zweitveröffentlichungen 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  -