Synchronization in systems with nonlocal interactions

Lutz Schimansky-Geier

Humboldt Universität zu Berlin

We consider models of activity of single neurons which are defined by their waiting time density. Examples of densities and dynamical properties of neurons as detectability will be discussed. These waiting time densities determine also the dynamics if interacting neurons cluster to ensembles. The interaction is due to nonlocal kernels in field equations for the probability distribution density of the neuronal activity. Their derivation is shown by example. Phenomena like wave propagation, synchronization and anesthetics are traced back to bifurcation phenomena of the nonlocal field equations.

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