Population density models of integrate-and-re neurons with jumps

In this paper we study the well-posedness of dierent models of population of leaky integrate- and-re neurons with a population density approach. The synaptic interaction between neurons is mod- eled by a potential jump at the reception of a spike. We study populations that are self excitatory or self inhibitory. We distinguish the cases where this interaction is instantaneous from the one where there is a repartition of conduction delays. In the case of a bounded density of delays both excitatory and inhibitory population models are shown to be well-posed. But without conduction delay the solution of the model of self excitatory neurons may blow up. We analyze the dierent behaviours of the model with jumps compared to its diusion approximation.