32447
2006
2006
eng
article
1
--
--
--
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
5522
2006
eng
postprint
0
2011-12-13
--
--
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.
urn:nbn:de:kobv:517-opus-57231
5723
Europhysics Letters: a letters journal exploring the frontiers of physics. - ISSN 0295-5075. - 75 (2006), 4, S. 535 - 541
first published in:<br/>
<a href="https://www.epletters.net/4DCGI/_general&presentation/-1/0/0/0/0/0/404054498">Europhysics Letters: a letters journal exploring the frontiers of physics</a><br/>
<a href="http://dx.doi.org/10.1209/epl/i2006-10147-0"<DOI: 10.1209/epl/i2006-10147-0</a><br/>
EDP Sciences
Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Marco Thiel
Maria Carmen Romano
Jürgen Kurths
Martin Rolfs
Postprints der Universität Potsdam : Humanwissenschaftliche Reihe
paper 264
Sprache
open_access
Institut für Psychologie
Institut für Physik und Astronomie
Universität Potsdam
https://publishup.uni-potsdam.de/files/5522/phr_264_2011_12_13.pdf
12025
2006
2006
eng
article
1
--
--
--
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
http://www.springerlink.com/content/102972
10.1007/s11071-006-1957-x
0924-090X
allegro:1991-2014
10101821
Nonlinear dynamics. - ISSN 0924-090X. - 44 (2006), 1-4, S. 135 - 149
Jürgen Kurths
Maria Carmen Romano
Marco Thiel
Grigory V. Osipov
Mikhail V. Ivanchenko
Istvan Z. Kiss
John L. Hudson
Institut für Physik und Astronomie
Referiert
Institut für Physik
34319
2006
2006
eng
article
1
--
--
--
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
Institut für Psychologie
15384
2004
2004
eng
article
1
--
--
--
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
0218-1274
allegro:1991-2014
10104079
International Journal of Bifurcation and Chaos. - ISSN 0218-1274. - 14 (2004), 6, S. 2107 - 2114
M. Thiel
Maria Carmen Romano
Udo Schwarz
Jürgen Kurths
Jens Timmer
Institut für Physik und Astronomie
Referiert
Institut für Physik
12170
2006
2006
eng
article
1
--
--
--
Spurious structures in recurrence plots induced by embedding
In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay
10.1007/s11071-006-2010-9
allegro:1991-2014
10101822
Nonlinear dynamics. - 44 (2006), 1-4, S. 299 - 305
Marco Thiel
Maria Carmen Romano
Jürgen Kurths
Institut für Physik und Astronomie
Referiert
Institut für Physik
46058
2006
2006
eng
3567
3579
13
12
16
article
World Scientific Publ. Co
Singapore
1
2006-01-04
2006-01-04
--
Shrimp structure and associated dynamics in parametrically excited oscillators
We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.
International journal of bifurcation and chaos : in applied sciences and engineering
10.1142/S0218127406016987
0218-1274
wos:2006
WOS:000244615800006
Zou, Y (reprint author), Univ Potsdam, Neuen Palais 10, D-14469 Potsdam, Germany., yong@agnld.uni-potsdam.de
importub
2020-04-16T14:24:54+00:00
filename=package.tar
1f810c993080859657b81b1bc493147e
false
true
Yong Zou
M. Thiel
Maria Carmen Romano
Jürgen Kurths
Q. Bi
eng
uncontrolled
bifurcation analysis
eng
uncontrolled
recurrence plot
eng
uncontrolled
period doubling
eng
uncontrolled
intermittency
Physik
Institut für Physik und Astronomie
Referiert
Institut für Physik
Import
18682
2001
2001
eng
article
1
--
--
--
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.
0004-640x
allegro:1991-2014
10095412
Astrophysics and space science. - ISSN: 0004-640x. - (Supplement 1). - 276 (2001), S. 187 - 188
Marco Thiel
Maria Carmen Romano
Udo Schwarz
Jürgen Kurths
Günther Hasinger
Tomaso Belloni
Interdisziplinäres Zentrum für Dynamik komplexer Systeme
15303
2004
2004
eng
article
1
--
--
--
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
0375-9601
allegro:1991-2014
10103734
Physics Letters A. - ISSN 0375-9601. - 330 (2004), 3-4, S. 214 - 223
Maria Carmen Romano
Marco Thiel
Jürgen Kurths
Werner von Bloh
Institut für Physik und Astronomie
Referiert
Institut für Physik
31882
2009
2009
eng
article
1
--
--
--
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
15382
2004
2004
eng
article
1
--
--
--
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
0375-9601
allegro:1991-2014
10104077
Physics Letters A. - ISSN 0375-9601. - 330 (2004), 5, S. 343 - 349
M. Thiel
Maria Carmen Romano
Jürgen Kurths
Institut für Physik und Astronomie
Referiert
Institut für Physik
10612
2008
2008
eng
article
1
--
--
--
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
Institut für Psychologie
Referiert
5489
2006
eng
postprint
0
2011-12-07
--
--
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.
urn:nbn:de:kobv:517-opus-56906
5690
Philosophical Transactions of the Royal Society - Series A. - ISSN 1471-2962. - 366 (2008), S. 545-557
first published in: <br/>
<a href="http://rsta.royalsocietypublishing.org/">Philosophical Transactions of the Royal Society - Series A</a> (2008), 366 : S. 545-557 <br/>
<a href="http://dx.doi.org/10.1098/rsta.2007.2109">DOI:10.1098/rsta.2007.2109</a> <br/>
Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Marco Thiel
Maria Carmen Romano
Jürgen Kurths
Martin Rolfs
Reinhold Kliegl
Postprints der Universität Potsdam : Humanwissenschaftliche Reihe
paper 238
eng
uncontrolled
Æ Recurrence Plots
eng
uncontrolled
Surrogate Data
eng
uncontrolled
Hypothesis Test
eng
uncontrolled
Phase Synchronization
Sprache
open_access
Institut für Psychologie
Institut für Physik und Astronomie
Universität Potsdam
https://publishup.uni-potsdam.de/files/5489/phr_238_2011_12_07.pdf
15383
2004
2004
eng
article
1
--
--
--
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
1054-1500
allegro:1991-2014
10104078
Chaos. - ISSN 1054-1500. - 14 (2004), 2, S. 234 - 243
M. Thiel
Maria Carmen Romano
P. L. Read
Jürgen Kurths
Institut für Physik und Astronomie
Referiert
Institut für Physik
13858
2005
2005
eng
article
1
--
--
--
Detection of synchronization for non-phase-coherent and non-stationary data
We present a new method to detect phase as well as generalized synchronization in a wide class of complex systems. It is based on the recurrences of the system's trajectory to the neighborhood of a former state in phase space. We illustrate the applicability of the algorithm for the paradigmatic chaotic Rossler system in the funnel regime and for noisy data, where other methods to detect phase synchronization fail. Furthermore, we demonstrate for electrochemical experiments that the method can easily detect phase and generalized synchronization in non-phase- coherent and even non-stationary time series
0295-5075
allegro:1991-2014
10104291
Europhysics Letters. - ISSN 0295-5075. - 71 (2005), 3, S. 466 - 472
Maria Carmen Romano
M. Thiel
Jürgen Kurths
Istvan Z. Kiss
J. L. Hudson
Institut für Physik und Astronomie
Referiert
Institut für Physik
18288
2001
2001
eng
article
1
--
--
--
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.
http://journals.worldscientific.com.sg/ijbc/11/1110/S0218127401003619.html
allegro:1991-2014
10093228
International journal of bifurcation and chaos. - 11 (2001), 10/11, S. 2567 - 2578
Maria Carmen Romano
Marco Thiel
Udo Schwarz
Jürgen Kurths
Holger Lange
M. Hauhs
Interdisziplinäres Zentrum für Dynamik komplexer Systeme