10612
2008
2008
eng
article
1
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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.
http://rsta.royalsocietypublishing.org/
1364-503X
allegro:1991-2014
10104217
Philosophical transactions of the Royal Society, A: mathematical, physical and engineering sciences. - ISSN 1364-503X. - 366 (2008), 1865, S. 545 - 557
Marco Thiel
Maria Carmen Romano
Jürgen Kurths
Martin Rolfs
Reinhold Kliegl
Referiert
Department Psychologie
Institut für Psychologie
32447
2006
2006
eng
article
1
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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
http://www.mendeley.com/research/twin-surrogates-to-test-for-complex-synchronisation/#page-1
10.1209/epl/i2006-10147-0
allegro:1991-2014
10101717
Europhysics Letters. - 75 (2006), 4, S. 535 - 541
Marco Thiel
Maria Carmen Romano
Jürgen Kurths
Martin Rolfs
Reinhold Kliegl
Referiert
Institut für Physik
Department Psychologie
31882
2009
2009
eng
article
1
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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.
http://ojps.aip.org/chaos/
10.1063/1.3072784
1054-1500
allegro:1991-2014
10108231
Chaos. - ISSN 1054-1500. - 19 (2009), 1, Art. 015108
Maria Carmen Romano
Marco Thiel
Jürgen Kurths
Konstantin Mergenthaler
Ralf Engbert
Referiert
Department Psychologie
34319
2006
2006
eng
article
1
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Synchronization Analysis and Recurrence in Complex Systems
978-3-527-40623-4
allegro:1991-2014
10111539
Handbook of time series analysis : recent theoretical developments and applications / Hrsg.: Börn Schelter ; Matthias Winterhalder ; Jens Timmer. - Weinheim : Wiley-VCH-Verl., 2006. - ISBN 978-3-527-40623-4. - S. 231 - 308
Maria Carmen Romano
Marco Thiel
Jürgen Kurths
Martin Rolfs
Ralf Engbert
Reinhold Kliegl
Department Psychologie
Institut für Psychologie