Nonlinear Average Consensus Over Circulating Directed Hypergraphs

Consensus dynamics are ubiquitous in control theory, with applications spanning from technological fields to social sciences. In this Letter, we evaluate the impact of higher-order, many-body interactions on the ability of the network to attain consensus. Modeling multi-body interactions with circulating directed hypergraphs, we provide for the first time global conditions for average consensus in the presence of time-varying and possibly non-smooth coupling protocols. Our results are then applied to study the effect of homophily in opinion dynamics.