Elenco seminari del ciclo di seminari
“MCKEAN-VLASOV MODELS FOR SYSTEMS OF SPIKING NEURONS”

This is a PhD mini-course which will unfold in 5 lectures by 2 hours each. We will introduce two basic processes describing systems of interacting and spiking neurons. In both processes, neurons spike at a rate depending on their membrane potential value. When spiking, they have a direct influence on their post-synaptic partners, namely, a fixed value, called "synaptic weight", is added to the potential of the postsynaptic neurons. In between successive spikes, due to some leakage effects, the membrane potential process follows a deterministic flow. In the first class of processes, the (non-linear) Hawkes processes, the membrane potential of the spiking neuron remains unchanged upon spiking, while in the second class of process, it goes back to a resting value inducing a discontinuity that we will refer to as "big jumps". The program is divided into 2 parts: Part I - Mean field limits of the Hawkes description of the model; Part II - Discontinuous model with big jumps.