TY - JOUR
A1 - Romano, Maria Carmen
A1 - Thiel, Marco
A1 - Kurths, Jürgen
A1 - Mergenthaler, Konstantin
A1 - Engbert, Ralf
T1 - Hypothesis test for synchronization : twin surrogates revisited
N2 - 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.
Y1 - 2009
UR - http://ojps.aip.org/chaos/
U6 - http://dx.doi.org/10.1063/1.3072784
SN - 1054-1500
ER -
TY - JOUR
A1 - Zou, Yong
A1 - Thiel, M.
A1 - Romano, Maria Carmen
A1 - Kurths, Jürgen
A1 - Bi, Q.
T1 - Shrimp structure and associated dynamics in parametrically excited oscillators
JF - International journal of bifurcation and chaos : in applied sciences and engineering
N2 - 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.
KW - bifurcation analysis
KW - recurrence plot
KW - period doubling
KW - intermittency
Y1 - 2006
U6 - http://dx.doi.org/10.1142/S0218127406016987
SN - 0218-1274
VL - 16
IS - 12
SP - 3567
EP - 3579
PB - World Scientific Publ. Co
CY - Singapore
ER -
TY - JOUR
A1 - Romano, Maria Carmen
A1 - Thiel, M.
A1 - Kurths, Jürgen
A1 - Kiss, Istvan Z.
A1 - Hudson, J. L.
T1 - Detection of synchronization for non-phase-coherent and non-stationary data
N2 - 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
Y1 - 2005
SN - 0295-5075
ER -
TY - JOUR
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 only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres.
Y1 - 2008
UR - http://rsta.royalsocietypublishing.org/
SN - 1364-503X
ER -
TY - JOUR
A1 - Kurths, Jürgen
A1 - Romano, Maria Carmen
A1 - Thiel, Marco
A1 - Osipov, Grigory V.
A1 - Ivanchenko, Mikhail V.
A1 - Kiss, Istvan Z.
A1 - Hudson, John L.
T1 - Synchronization analysis of coupled noncoherent oscillators
N2 - 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
Y1 - 2006
UR - http://www.springerlink.com/content/102972
U6 - http://dx.doi.org/10.1007/s11071-006-1957-x
SN - 0924-090X
ER -
TY - JOUR
A1 - Thiel, Marco
A1 - Romano, Maria Carmen
A1 - Kurths, Jürgen
T1 - Spurious structures in recurrence plots induced by embedding
N2 - 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
Y1 - 2006
U6 - http://dx.doi.org/10.1007/s11071-006-2010-9
ER -
TY - JOUR
A1 - Thiel, Marco
A1 - Romano, Maria Carmen
A1 - Schwarz, Udo
A1 - Kurths, Jürgen
A1 - Hasinger, Günther
A1 - Belloni, Tomaso
T1 - Nonlinear Time series analysis of the X-ray flux of compact objects
N2 - 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.
Y1 - 2001
SN - 0004-640x
ER -
TY - JOUR
A1 - Thiel, Marco
A1 - Romano, Maria Carmen
A1 - Kurths, Jürgen
A1 - Rolfs, Martin
A1 - Kliegl, Reinhold
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 Rossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems
Y1 - 2006
UR - http://www.mendeley.com/research/twin-surrogates-to-test-for-complex-synchronisation/#page-1
U6 - http://dx.doi.org/10.1209/epl/i2006-10147-0
ER -
TY - JOUR
A1 - Romano, Maria Carmen
A1 - Thiel, Marco
A1 - Kurths, Jürgen
A1 - Rolfs, Martin
A1 - Engbert, Ralf
A1 - Kliegl, Reinhold
T1 - Synchronization Analysis and Recurrence in Complex Systems
Y1 - 2006
SN - 978-3-527-40623-4
ER -
TY - JOUR
A1 - Thiel, M.
A1 - Romano, Maria Carmen
A1 - Schwarz, Udo
A1 - Kurths, Jürgen
A1 - Timmer, Jens
T1 - Surrogate-based hypothesis test without surrogates
N2 - 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
Y1 - 2004
SN - 0218-1274
ER -