SCL's Igor Franovic presented a seminar talk entitled:

"Statistical Physics of Neuronal Systems"

Abstract: Given the multiplicity of characteristic spatial and temporal scales, the complex multistage nature of interactions, the hierarchical modular organization as well as the wealth of emergent phenomena based on synchronization between the units’ activity, the neuronal systems may be regarded as the paradigmatic examples of complex systems. In this context, several basic notions, including the phase theory of synchronization, excitability, bursting, noise and time delay will be introduced in brief. The main focus of the talk will lie with the collective motion of ensembles whose local dynamics involves excitability or bursting, the two regimes of activity typical for biological neurons. Regarding the former, the extent of analogy between the self-organization phenomena in coupled phase oscillators and the ensembles of excitable units is examined by considering as an example the recent discovery on spontaneous formation of asymptotically stable or dynamical cluster states in homogeneous ensembles of excitable units influenced by noise and interaction delay. For the excitable systems, it will also be demonstrated how the stochastic stability and stochastic bifurcations which lead to the onset or the suppression of the collective mode can be characterized in terms of the deterministic mean-field model, based on the quasi- independence and Gaussian approximations. In case of bursting units, two types of results will be presented: apart from the qualitative and quantitative predictions of the appropriate mean-field model, the elements of the theory of complex networks will be used to analyze the relation between the structural and different forms of functional neuronal networks. For each of the considered topics, the aim will not only be to discuss the results already obtained, but also to point at the related problems whose solving would be of particular interest.