Bastian Pietras

General Interest

How can we describe and understand the dynamics of complex systems such as our brain? This question has been driving my still young research career. Within the realm of nonlinear dynamics, I study synchronization properties of neural networks. I want to understand how information is processed and transmitted, how different subnetworks interact with each other, and how microscopic dynamics translate into macroscopic behavior.

Current research

I am currently investigating dynamic correlations between oscillatory activity in the human brain. We use neuronal population models that are capable of generating large-scale oscillations and classify the mechanisms that lead to the latter by combining ideas from computational neuroscience, nonlinear dynamics, and statistical mechanics, as well as from mathematical modeling, and bifurcation theory.

Résumé

I received a Bachelor's and Master's degree in mathematics from the University of Münster, with minor studies in economics and psychology. In my thesis I investigated synchronization patterns of non-locally coupled oscillators, focussing mainly on their bifurcation and stability analysis. In 2015 I started my PhD research with Andreas Daffertshofer as part of the H2020 Marie Curie project COSMOS. Between 2016 and 2017, I spent one year in the Nonlinear and Biomedical Physics group at Lancaster University under the supervision of Aneta Stefanovska.

Frequency-doubling bifurcations in neuronal networks – a means of cross-frequency interactions

Neuronal populations often display oscillatory activity. Prominent examples for this are ~10 Hz alpha oscillations in the visual cortex and ~20 Hz be oscillations in the motor cortex. This project addresses whether switches between frequency bands on a macroscopic scale can be interpreted as frequency-doubling bifurcations or should be viewed as discrete switches between two different oscillations. Such sequential transitions can shed light on dynamic correlations between oscillatory activity in the human brain: by classifying bifurcation routes we may constrain symmetries and types of interactions between neurons and/or neuronal ensembles and thereby confine models.

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Other PHD Students

At a glance: All current PhD Students at Coordination Dynamics