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  - 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  - 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  - https://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, 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  - 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  -