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Synchronization and spontaneous dynamics in electrically coupled networks
Held by Dr. Georgi Medvedev (Department of
Mathematics, Drexel University, Philadelphia, USA)
12.12.2013, 16:00 Uhr
Direct electrical coupling through gap-junctions is a common way of
communication between neurons, as well as between cells of the heart,
pancreas, and other physiological systems. Electrical synapses are
important for synchronization of the network activity, wave
propagation, and pattern formation in neuronal networks.
In this talk, we present a mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise. Using the large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled networks. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior.