Prof. Marc Timme

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Networks of interacting units dominate our everyday lives, from the
dynamics of neural circuits that control our behaviors to the power
grids that provide us with electric energy. Over the last 15 years,
researchers furthered our understanding of complex networks by analyzing
their connectivity structure and collective dynamics, mostly using
perspectives from either graph theory, statistical physics or nonlinear
dynamics. Recent progress shows that features from the statistical physics and the
nonlinear dynamics of networks are often intimately related; I discuss
two main examples: Many different neural circuits exhibit
spatio-temporal activity patterns, but the dynamic origin of such
patterns remains unknown. I link the nonlinear deterministic dynamics of
such systems to a statistical description. The results indicate that
non-additive coupling, recently found in neuro-physiological
experiments, enable the generation of spike patterns in circuits
consistent with anatomy. In a second example, I identify a type of percolation transition that
was unknown so far. Analyzing the microscopic dynamics of link additions
reveals that the transition is continuous in the thermodynamics limit
but discontinuous features prevail even for macroscopic finite systems.
Finally, I briefly mention a new concept of universal computation via
switching in complex networks of states and the intriguing
self-organized dynamics of power grids.

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MPI for Dynamics and Self-Organization
Seminarraum Theoretische Physik
Contact: not specified