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Talk Abstract

Synchrony of large sparse neuronal networks

Synchrony of large sparse neuronal networks

We study synchronization in large populations
of *N* identical neurons with random sparse connectivity. Synchrony
occurs only when the average number of synapses *M* a cell receives is larger
than a critical value *M _{c}*. Below

In the limit of weak coupling, we use the
averaging method to reduce the network model into a model of phases which
are coupled via a function of their phase differences.
Using mean field theory,
we show that the stability of the asynchronized state can be determined exactly
in the asymptotic limit * 1<< M _{c} << N*. In particular we
establish that in this limit

We apply our analytical theory to study
integrate-and-fire neurons with inhibitory coupling.
We find that *M _{c}* varies non-monotonously with the level
of the external input on the neuron,
that it is a strongly decreasing function of the
the synaptic rise time and of the duration of the refractory period
of the neuron.
For typical inhibitory synapses and refractory period of
2-5 msec we find that

We conclude by discussing the relevance of our theory to understand the mechanisms of synchrony in neocortex and hippocampus and by proposing experiments to test it.