**Synchrony in stochastic pulse-coupled neuronal network models
**

Katie Newhall

Rensselaer Polytechnic Institute

Department of Mathematics

Many pulse-coupled dynamical systems possess synchronous attracting states. Even stochastically driven model networks of Integrate and Fire neurons demonstrate synchrony over a large range of parameters.
We study the interplay between fluctuations which de-synchronize and
synaptic coupling which synchronizes the network by calculating the
probability to see repeated cascading total firing events,
during which all the neurons in the network fire at once. The mean
time between total firing events characterizes the perfectly
synchronous state, and is computed from a first-passage time problem
in terms of a Fokker-Planck equation for a single neuron.