The Group Nichtlineare Dynamik addresses topics in the research of complex nonlinear systems especially focusing on theoretical methods. Nonlinear dynamics is an interdisciplinary field of science which combines physics and mathematics with many other sciences. An important objective of our work is the immediate mutual interaction of our theoretical investigations and particular applications, as there are cosmic structure formation, problems of environmental research or even aspects of medicine and psychology. In the field of medicine it is of our interest, particularly, the 2D and 3D quantification of bone structure and its changes in microgravity condition by measures of complexity, the analysis of heart-rate-variability in connection with a predictive recognition of high-risk patients for the sudden cardiac death, and the diagnosis of Parkinson disease by means of synchronization analysis. In the field of psychology it is the cognitive complexity.
Nonlinear processes far from thermodynamical equilibrium can exhibit a richness of stable and unstable structures. Such systems are not at all exceptions from the rule but, quite the contrary, are very common in nature. Their investigation has revealed unexpected new insights, important even for epistemology which led to new paradigms. A well recognized fact are those deterministic processes which exhibit a behavior - the so-called Deterministic Chaos - structurally so complex that long-term forecasts fail. Such systems undergo unforeseeable irregular developments. In such cases small causes carry along severe effects. This behavior is very typical for feedback-systems: e. g. for the interactions of humans with their environment or the relation between health and the way of living.
Investigation of such nonlinear dynamics is still at the beginning. As it is still frequently based on oversimplified assumptions, one of our essential aims is to develop methods to treat such processes more adequately with respect to reality. In this direction we are working on the following fundamental aspects:
Theoretical studies on phase synchronization of chaotic systems. We have developed synchronization based approach to bivariate data analysis. It allows to reveal weak interaction between oscillatory objects from data and quantify strength and direction of interaction. These methods have been applied to brain activity of Parkinson patients, cardiorespiratory synchronization in healthy athletes and newborns, or to spatiotemporal dynamics of ecological systems.
Complex spatio-temporal dynamics as an aproach towards the understanding of turbulence. This is one of the fundamental problems in physics of which we investigate both high dimensional systems, described by partial differential equations (PDE) and weak turbulence in distributed systems. We develop numerical methods for the non-simulative analysis of the qualitative behavior (bifurcations etc.) of complex systems. This approach has been applied to ocean dynamics and scalar activity.
Noise-induced effects which lead to ordering in nonlinear systems. We focus on topics of noise-induced effects in physics, chemistry and biology. Such important and counterintuitive phenomena as noise-induced phase transitions, stochastic resonance, coherence resonance, and structure formation are investigated. Out theoretical results are applied to oscillating systems, e.g. epidemiological models, or a model of El-Nino oscillation, turbulence, signal processing, molecular motors in biological cells, and chemical reactions.
Another point of interest of our work are nonlinear methods for the analysis of experimental data, which links theoretical research to specific applications. The main goal hereof is to determine properties from the experimental data which underlie the observed phenomena. As opposed to experiments in the laboratory where the circumstances are generally well controllable, measurements in natural systems (like astro- or geophysics or physiology) additionally challenge data analysis: a typical difficulty is the irreproducibility of such measurements or that these observations often refer to transient phenomena. Consequently, we deal with the problem of stationarity. A very promising approach to characterize such data are complexity measures, recurrence plots, or synchronization analysis.
The activity of the group is closely related to the Center for Dynamics of Complex Systems. The goal of the Center for Dynamics of Complex Systems is to further interdisciplinary research and teaching in the field of Nonlinear Dynamics and Complex Systems. We study in interdisciplinary collaboration the behavior of complex systems using methods of nonlinear dynamics and statistical physics. Beyond the development of new methods, we focus on applications of the theoretical results in a variety of different areas of physics and life. The Center puts its emphasis on organization of scientific cooperation in interdisciplinary research. Its activity also includes distribution of funds and preparation of new projects.
The Interdisciplinary Center for Dynamics of Complex Systems uses the resources of these departments to achieve synergy effects by virtue of common interdisciplinary research projects:
EU Research Training Network "Control and Synchronization of Spatially Extended Nonlinear Systems"
DFG - Schwerpunktprogramm 1114 "Mathematische Methoden der Zeitreihenanalyse und digitalen Bildverarbeitung"
SFB 555 "Komplexe nichtlineare Prozesse - Analyse, Simulation, Steuerung und Optimierung"
We organized several workshops and conferences, mainly to mention:
The researchers of the center have access to high level software tools like Mathematica, IDL and Matlab. The scientific library holds the main journals in the relevant fields. The electronic versions of these journals are available online. The center frequently hosts highly qualified researchers from worldwide coming for a short visit to give lectures and to exchange expertise.
Currently the Center for Dynamics of Complex Systems has almost 50 members from different university departments (biology, chemistry, general linguistics, geosciences, informatics, mathematics, physics, psychology) and research institutes (GeoForschungsZentrum Potsdam, Potsdam-Institut fuer Klimafolgenforschung, Alfred-Wegener-Institut fuer Polar- und Meeresforschung, Astrophysikalisches Institut Potsdam, Deutsches Institut fuer Ernaehrungsforschung).