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Institute of MathematicsInstitute of Information TechnologyInstitute of PhysicsInstitute of ChemistryInstitute of Biology and BiochemistryInstitute of Nutritional ScienceInstitute of GeographyInstitute of GeoecologyInstitute of Earth Sciences
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Faculty of Mathematics and Sciences
Institut
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close  Research

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close  Nonlinear Dynamics

Many phenomena in nature and engineering exhibit complex and chaotic behaviour, such as turbulence or neuronal activities. The application of linear methods used to describe such processes is usually insufficient. Therefore, it is necessary to consider higher-order (nonlinear) terms. The investigation of nonlinear processes yields to multifaceted complex solutions, which could be found and studied only after the progressive evolution of computer power in the last decades.

Research groups:

external link  Nonlinear Dynamics

The nonlinear dynamics deals with phenomena which cannot be described by linear models. This work contains the investigation of chaotic, complex systems with methods looking particularly for nonlinear properties (and the development of such methods) as well as the modelling of nonlinear, complex processes.

The research of this interdisciplinary chair covers a variety of scientific disciplines such as astrophysics, earth and life sciences and engineering: modelling of planetary rings (Saturn moons) and solar activity, studies of modern and past climate, oceanography, earthquakes, cognitive sciences, neuronal networks, cardiac diseases, osteoporosis research or system biology. The main focus lies in modelling, synchronisation and recurrence analysis, complex networks and time series analysis. The strong international cooperations and very successful fundraising are powerful advantages of the work of this group withal.

group leader: internal link Prof. Dr. Ralf Metzler

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external link  Statistical Physics / Theory of Chaos

Complex systems are abundant in nature (climate and weather, turbulence, granular materials, environment) or are a product of the social activity (traffic, macro-economy, internet, telecommunication). Complexity deals both with the network organization as well as with the dynamics of these systems.

Classical statistical physics treats many-body systems in equilibrium, however, complex systems are typically nonequilibrium ones. Analysis of such phenomena is not only a challenging intellectual task, but has many practical applications. Complexity results quite often in the chaotic dynamics. The task of the theory of chaos is in finding general laws of chaos, applicable to systems of different origin. Many problems in the field of complexity can be treated with the help of massive numerical simulations only, typically in a combination with deep mathematical methods.

The present research topics of the group include chaos and its synchronization, statistical description and control of complex systems, effects of noise, data analysis, dynamics between chaos and order, space-time dynamics and pattern formation.

group leader: internal link Prof. Dr. Arkadi Pikovski

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