# Mathematics Colloquia and Seminars

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### Synchrony-breaking and Rare Events in Stochastic Neuronal Networks

**PDE and Applied Math Seminar**

Speaker: | R.E. Lee Deville, University of Illinois, Urbana-Champaign |

Location: | 1147 MSB |

Start time: | Tue, Jan 12 2010, 4:10PM |

We consider a model for a network of pulse-coupled oscillators containing randomness both in input and in network architecture. We analyze the scalings which arise in certain limits and interpret various "finite-size" effects as perturbations of these limits. Most notably, for certain parameters, this network supports both synchronous and asynchronous modes of behavior and will switch stochastically between these modes due to rare events. We also relate the analysis of this network to classical results in graph theory, and in particular, those involving the size of the "giant component" in the Erdos-Renyi random graph. This work is joint with Charles Peskin and Joel Spencer.