Nonlinear Dynamics and Time Series Analysis

Welcome to the web-page of our research group


Irregular temporal behaviour is ubiquitious in the world surrounding us:
wind speeds, water wave heights, stock market prices, exchange rates,
blood pressure, or heart rate all fluctuate more or less irregularly in time.
Such signals are the output of quite complex systems with
nonlinear feedback loops and external driving.
Our goal is to quantify, understand, model, and
predict such irregular fluctuations. Therefore, our research includes the
study of deterministic and stochastic model systems which are selected because
of interesting dynamical/statistical behaviour and which serve as paradigmatic
data models.  We design data analysis
methods, we design tests and measures of performance for such
methods, and we apply these to data sets with various properties. Last but not
least, we study data sets because we wish to understand the underlying
phenomena and to improve data based predictions of fluctuations.
Out of the initially listed examples of data sources, the atmosphere sticks
out for two reasons: On the one hand, the atmosphere is an exciting highly
complex physical system, where many different sub-fields of physics meet:
Hydrodynamical transport, thermodynamics, light-matter interaction, droplett
formation, altogether forming a system which is not only far from equilibrium
but also far from a linear regime around some working point. On the other
hand, climate change and the impact of extreme weather on human civilization
give atmospheric physics a high relevance. Since the only perfect model of the
atmosphere is the real world itself, and since due to very strong
nonlinearities and hierarchical structures
the misleading effects of any approximation might be tremendous, a data based
approach to climate issues is urgently needed as a complement to simulating
 climate by models.

In a broader context, our work can also seen as part of
what nowadays is called data science: We make huge data sets
 accessible to our studies, we design visualization concepts and
analysis tools, we test hypothesis,
construct models, and apply forecast schemes similar to machine learning.
The time series aspect enters our work through the fact that
 the temporal order in which data are recorded carries part of the
 information, and physics enters as background information, constraints, and
reference models.