Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, May 26, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Angelika Steger

Synchrony and Asynchrony in Neural Networks

In this talk we pick up on a model described recently by DeVille and Peskin (Bulletin of Mathematical Biology, to appear) for a stochastic pulsecoupled neural network. The key feature and novelty in their approach is that they describe the interactions of a neuronal system as a discrete-state stochastic dynamical network. They show (experimentally and by some estimates in an associated mean-field limit of the model) that their network can exhibit both synchronous and asynchronous behavior. They also exhibit a range of parameters for which the network switches seemingly spontaneously between synchrony and asynchrony. In synchronous behavior the firing of one neuron leads to the firing of other neurons, which in turn may set off a chain reaction that often involves a substantial proportion of the neurons. There are strong analogies to the giant component phenomenon in random graph theory.

In this talk we present a rigorous analysis of the model of DeVille and Peskin thereby answering in particular their questions about the actual parameter settings resp. thresholds for which these changes between synchronous and asynchronous behavior occur. We also provide insights into the coexistence of synchronous and asynchronous behavior and the conditions that trigger a 'spontaneous' transition from one state to another.

Joint work with Fabian Kuhn, Konstantinos Panagiotou, and Joel Spencer.

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