Colloquium Talk

The dynamics of interacting biological neurons is commonly described through multi-agent models on graphs. We only assume an extended mean-field scaling but otherwise allow any arbitrary choice of synaptic weights. We are nevertheless able to identify an emerging structure through a new notion of extended graphons and novel regularity estimates on the system. This allows to derive limiting equations that are similar to the famous neural field models, but without having to assume some redefined spatial structure on the connection maps between neurons. Even more remarkably, the new trajectories of individual neurons and to quantify how similar two neurons are. This corresponds to a series of joint work with D. Poyato, V. Schmutz, J. Soler, and D. Zhou.