Simultaneous jumps in interacting particle systems: From neuronal networks to a general framework

This paper comes as a survey of the links between recent works on particle systems with simultaneous jumps and the neuroscience literature. We consider systems of N weakly interacting diffusions with jumps, having the peculiar feature that the jump of one component may induce simultaneous jumps of all others. While models belonging to this class have been proposed for the dynamics of neuronal systems, and their limiting (N → +∞) behavior has been studied for some special cases, recently a study of propagation of chaos and of the corresponding McKean-Vlasov equation has appeared in a general framework. Here we justify the link between this approach and the neuronal models.