TY  - THES
A1  - Zou, Yong
T1  - Exploring recurrences in quasiperiodic systems
T1  - Untersuchung des Wiederkehrverhaltens in quasiperiodischen dynamischen Systemen
N2  - In this work, some new results to exploit the recurrence properties of quasiperiodic dynamical systems are presented by means of a two dimensional visualization technique, Recurrence Plots(RPs). Quasiperiodicity is the simplest form of dynamics exhibiting nontrivial recurrences, which are common in many nonlinear systems. The concept of recurrence was introduced to study the restricted three body problem and it is very useful for the characterization of nonlinear systems. I have analyzed in detail the recurrence patterns of systems with quasiperiodic dynamics both analytically and numerically. Based on a theoretical analysis, I have proposed a new procedure to distinguish quasiperiodic dynamics from chaos. This algorithm is particular useful in the analysis of short time series. Furthermore, this approach demonstrates to be efficient in recognizing regular and chaotic trajectories of dynamical systems with mixed phase space. Regarding the application to real situations, I have shown the capability and validity of this method by analyzing time series from fluid experiments.
N2  - In dieser Arbeit stelle ich neue Resultate vor, welche zeigen, wie man Rekurrenzeigenschaften quasiperiodischer, dynamischer Systeme für eine Datenanalyse ausnutzen kann. Die vorgestellten Algorithmen basieren auf einer zweidimensionalen Darstellungsmethode, den Rekurrenz-Darstellungen. Quasiperiodizität ist die einfachste Dynamik, die nicht-triviale Rekurrenzen zeigt und tritt häufig in nichtlinearen Systemen auf. Nicht-triviale Rekurrenzen wurden im Zusammenhang mit dem eingeschränkten Dreikörper-problem eingeführt. In dieser Arbeit, habe ich mehrere Systeme mit quasiperiodischem Verhalten analytisch untersucht. Die erhaltenen Ergebnisse helfen die Wiederkehreigenschaften dieser Systeme im Detail zu verstehen. Basierend auf den analytischen Resultaten, schlage ich einen neuen Algorithmus vor, mit dessen Hilfe selbst in kurzen Zeitreihen zwischen chaotischem und quasiperiodischem Verhalten unterschieden werden kann. Die vorgeschlagene Methode ist besonders effizient zur Unterscheidung regulärer und chaotischer Trajektorien mischender dynamischer Systeme.Die praktische Anwendbarkeit der vorgeschlagenen Analyseverfahren auf Messdaten, habe ich gezeigt, indem ich erfolgreich Zeitreihen aus fluid-dynamischen Experimenten untersucht habe.
KW  - Wiederkehrverhalten
KW  - quasiperiodisches dynamisches System
KW  - Recurrence Plot
KW  - recurrence
KW  - quasiperiodic dynamical systems
KW  - recurrence plots
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16497
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  - Donges, Jonathan
A1  - Zou, Yong
A1  - Marwan, Norbert
A1  - Kurths, Jürgen
T1  - Complex networks in climate dynamics : comparing linear and nonlinear network construction methods
N2  - Complex network theory provides a powerful framework to statistically investigate the topology of local and non- local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.
Y1  - 2009
UR  - http://www.springerlink.com/content/1951-6355
U6  - https://doi.org/10.1140/epjst/e2009-01098-2
SN  - 1951-6355
ER  -