Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Statistical Analysis and Stochastic Modelling of Complex Systems

Head of group:  Eule, Stephan 

The dynamics of many systems in nature is too complicated to be described ab initio. Today, the investigation of such complex systems plays an important role, not only in physics, but in many fields of science. In general, such systems are in a state far from equilibrium, i. e. they are exposed to a constant flux of energy. Therefore, a common feature of complex systems is the occurrence of intricate fluctuations which can be induced either by a complex environment or stem from internal dynamics. To describe these systems, one applies the mathematical theory of stochastic processes. The research interests of our group range from the application of stochastic processes to biological, ecological and socio-economic systems to the mathematical generalization of stochastic processes to account for systems which exhibit anomalous diffusion. Thereby an interdisciplinary approach is employed, applying methods from statistical mechanics, network theory and game theory.


Statistical Properties of Order Books

In recent years there have been considerable efforts to employ methods from theoretical physics to problems in economics. Our group is interested in the dynamics of the order book, which can be seen as the ultimate microscopic level of description of financial markets.

Dynamics and Control of Infectious Diseases

The sudden appearance and rapid spread of an infectious diseases can pose a serious threat to human or animal populations that calls for immediate actions by national and international health agencies. Their response is guided by epidemiological models whose primary use is to provide means of comparing the effectiveness of different containment strategies. The focus of our group is to quantify, how heterogeneity of the infection process affects the course of an infectious disease. In particular, we are interested in the effect of indiviudal variation in disease transmission on control strategies in the early phase of an epidemic outbreak and the consequences of spatially varying infection rates on travel restrictions.

Anomalous Stochastic Processes

If the time-evolution of the mean-squared displacement of some quantity is non-linear, the system is said to exhibit anomalous diffusion. The underlying mechanisms leading to such anomalous diffusion can be multifold. Our group focuses on processes whose anomalous behavior is due to heavy-tailed distributions of either the waiting time distribution between the displacements or of the displacements themselves.

People working in this Group:

Name Email Phone
Stephan Eule send email   [+49-(0)551-5176-411
Theo Geisel send email   [+49-(0)551-5176-400
Nicolas Lenner send email   [+49-(0)551-5176-421