On the dynamics of large spiking neuronal networks

Jonathan Toubol

In this talk I will introduce new methods to investigate the limit and
dynamics of random integrate-and-fire neurons, and propose an explanation for
the emergence of power-law and universal scalings in neuronal data.  On the
theoretical side, I will consider a model in which neurons are intrinsically
noisy and fire as state-dependent Poisson processes.  I will show that if
neurons do not spontaneously fire, the network almost surely dies out for any
finite number of cells, but in the limit of large network size, self-sustained
(asynchronous irregular) activity and multiple invariant distribution may
appear.  I will pursue by showing that in synchronous irregular regimes, the
distribution of avalanches may have all criteria of critical systems, although
the system is not at a phase transition.  These two topics are joint works
with Ph. Robert and A. Destexhe.