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  - https://doi.org/10.1209/epl/i2006-10147-0
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  - https://doi.org/10.1007/s11071-006-1957-x
SN  - 0924-090X
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, 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  - https://doi.org/10.1007/s11071-006-2010-9
ER  - 
TY  - JOUR
A1  - Assmann, Birte
A1  - Thiel, Marco
A1  - Romano, Maria Carmen
A1  - Niemitz, Carsten
T1  - Recurrence plot analyses suggest a novel reference system involved in newborn spontaneous movements
JF  - Behavior research methods : a journal of the Psychonomic Society
N2  - The movements of newborns have been thoroughly studied in terms of reflexes, muscle synergies, leg coordination, and target-directed arm/hand movements. Since these approaches have concentrated mainly on separate accomplishments, there has remained a clear need for more integrated investigations. Here, we report an inquiry in which we explicitly concentrated on taking such a perspective and, additionally, were guided by the methodological concept of home base behavior, which Ilan Golard developed for studies of exploratory behavior in animals. Methods from nonlinear dynamics, such as symbolic dynamics and recurrence plot analyses of kinematic data received from audiovisual newborn recordings, yielded new insights into the spatial and temporal organization of limb movements. In the framework of home base behavior, our approach uncovered a novel reference system of spontaneous newborn movements.
Y1  - 2006
U6  - https://doi.org/10.3758/BF03192793
SN  - 1554-351X
SN  - 1554-3528
VL  - 38
IS  - 3
SP  - 400
EP  - 406
PB  - Springer
CY  - New York
ER  -