Title: Oscillation of the exit time distribution from an attractor, role of the second eigenvalue and application in Neurobiology.
<strong>Abstract:</strong> Neuronal networks can generate complex patterns of activity, yet we do not understand them. I will present a model based on synaptic properties and connectivity of the neuronal network and analyze the responses to single electrical stimulation of neuronal ensembles from small (between 2-20 cells in a restricted sphere) and large (acute hippocampal slice) networks. We found that the time for the neuronal potential of connected neurons to stay in a Up-state (depolarized) is non Poissonian. This behavior is not accounted for by any previous analysis of stochastic perturbation of a dynamical system. To resolve the origin of this phenomenon, I will present a singular perturbation analysis of the associated Fokker-Planck equation and a computation of the entire spectrum of this nonself-adjoint operator, using boundary layer methods.