Dynamics on random graphs

Systems involving interacting nodes are ubiquitous, arising in among other places biological, social and computer networks. Motivated by an example arising during development of neuronal networks, I will discuss the problem of finding periodic solutions on random graphs. In particular, we are interested in exploring what structural features of the graph are most likely to sustain periodic activity. The answer turns out to depend in surprising and non-intuitive ways on the type of dynamics that exist at each node and also the rules for interaction between nodes. No prior knowledge of neuronal networks or random graphs is needed to follow this talk.