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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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Prof. Marc Timme, MPI for Dynamics and Self-Organization
Seminarraum Theoretische Physik
Contact: not specified