: A cascading mean-field interacting particle system describing neuronal behavior.

Stochastic Analysis Seminar Series

We will introduce a particle system interacting through a mean-field term that models the behavior of a network of excitatory neurons.  The novel feature of the system is that the it features a threshold dynamic: when a single particle reaches a threshold,  it is reset while all the others receive an instantaneous kick. We show that in the limit  when the size of the system becomes infinite, the resulting non-standard equation of  McKean Vlasov type has a solution that may exhibit a blow-up phenomenon depending on the strength of the interaction, whereby a single particle reaching the threshold may cause a macroscopic cascade.  We moreover show that the particle system does indeed exhibit  propagation of chaos, and propose a new way to give sense to a solution after a blow-up.  

This is based on joint research with F. Delarue (Nice), E. Tanré (INRIA) and S. Rubenthaler (Nice).



Monday, May 19, 2014 - 14:15
to 15:15