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Applied Mathematics Seminar
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Mikhail I Rabinovich
Institute for Nonlinear Science, University of California San Diego

Neuronal Synchrony: Peculiarity & Generality

Wednesday 18th June 14:05-14:55pm, Carslaw 173.

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multi-dimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their 'dynamical repertoire' includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neural oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neural networks with plastic (STDP) synapses, (ii) synchronization of bursts that are generated by a group of non-symmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks, and (iv) coarse grained synchronization in larger systems.